For the circuit in Fig. P7.46, find (in joules): a) the total energy dissipated in the

The switch in the circuit shown has been closed for a long time and is opened at t = 0. a) Calculate the initial value of i. b) Calculate the initial energy stored in the inductor. c) What is the time constant of the circuit for t > 0? d) What is the numerical expression for i{t) for t > 0? e) What percentage of the initial energy stored has been dissipated in the 2 fl resistor 5 ms after the switch has been opened

At t = 0, the switch in the circuit shown moves instantaneously from position a to position b. a) Calculate v for t a 0+ . b) What percentage of the initial energy stored in the inductor is eventually dissipated in the 4 D, resistor?

The switch in the circuit shown has been closed for a long time and is opened at t = 0. Find a) the initial value of v(t), b) the time constant for t > 0, c) the numerical expression for v(t) after the switch has been opened, d) the initial energy stored in the capacitor, and e) the length of time required to dissipate 75% of the initially stored energy. 20kft -#AA/V 50 Ml

The switch in the circuit shown has been closed for a long time before being opened at t = 0. a) Find v0{t) for t > 0. b) What percentage of the initial energy stored in the circuit has been dissipated after the switch has been open for 60 ms?

Assume that the switch in the circuit shown in Fig. 7.19 has been in position b for a long time, and at t = 0 it moves to position a. Find (a) /-(0+ ); (b) v(0+ ); (c) T,t > 0; (d) i(t), t > 0; and (e) v(t), t > 0+ . NOTE: Also try Chapter Problems 7.35-737.

a) Find the expression for the voltage across the 160 kfi resistor in the circuit shown in Fig. 7.22. Let this voltage be denoted vA, and assume that the reference polarity for the voltage is positive at the upper terminal of the 160 kH resistor. NOTE: Also try Chapter Problems 7.51 and 7.53. b) Specify the interval of time for which the expression obtained in (a) is valid.

In the circuit shown, switch 1 has been closed and switch 2 has been open for a long time. At t = 0, switch 1 is opened. Then 10 ms later, switch 2 is closed. Find a) vc(t) for 0 < f < 0.01 s, b) vc(t) for t > 0.01 s, c) the total energy dissipated in the 25 kft resistor, and d) the total energy dissipated in the 100 kO resistor. ( U 60kn r=10 m " )10mAf40kft 25kftlAtF

Switch a in the circuit shown has been open for a long time, and switch b has been closed for a long time. Switch a is closed at t = 0 and, after remaining closed for 1 s, is opened again. Switch b is opened simultaneously, and both switches remain open indefinitely. Determine the expression for the inductor current i that is valid when (a)0sf< h and (b) t > 1 s.

There is no energy stored in the capacitor at the time the switch in the circuit makes contact with terminal a. The switch remains at position a for 32 ms and then moves instantaneously to position b. How many milliseconds after making contact with terminal a does the op amp saturate?

In the circuit shown in Fig. P7.ll, the switch has PSPICE been in position a for a long time. At t 0, it moves MULTISIM instantaneously from a to b. a) Find ia(t) for t > 0. b) What is the total energy delivered to the 8 fi resistor? c) How many time constants does it take to deliver 95% of the energy found in (b)?

The switch in the circuit in Fig. P7.12 has been in PSPICE position 1 for a long time. At t - 0, the switch moves MULTISIM instantaneously to position 2. Find v0(t) for t > 0+ . Figure P7.12 12 a AAA1 4a -vw72 mH 240 V 40a 10a: 6a

For the circuit of Fig. P7.12, what percentage of the initial energy stored in the inductor is eventually dissipated in the 40 O, resistor?

The switch in Fig. P7.14 has been closed for a long time before opening at t = 0. Find a) iL(t), t > 0. b) vL(t), t > 0+ . c) Ut), t > 0+ .

What percentage of the initial energy stored in the inductor in the circuit in Fig. P7.14 is dissipated by the 60 Q, resistor?

The switch in the circuit in Fig. P7.16 has been PSPICE closed for a long time before opening at t = 0. Find MULT,SIM v0(t) for r>0 + .

The 240 V, 2 ft source in the circuit in Fig. P7.17 is PSPICE inadvertently short-circuited at its terminals a,b. At 1 the time the fault occurs, the circuit has been in operation for a long time. a) What is the initial value of the current /ah in the short-circuit connection between terminals a,b? b) What is the final value of the current /ab? c) How many microseconds after the short circuit has occurred is the current in the short equal to 114 A?

The two switches in the circuit seen in Fig. P7.18 are synchronized. The switches have been closed for a long time before opening at t = 0. a) How many microseconds after the switches are open is the energy dissipated in the 4 kO, resistor 10% of the initial energy stored in the 6 H inductor? b) At the time calculated in (a), what percentage of the total energy stored in the inductor has been dissipated?

The two switches shown in the circuit in Fig. P7.19 PSPICE operate simultaneously. Prior to t = 0 each switch has been in its indicated position for a long time. At t 0 the two switches move instantaneously to their new positions. Find a) v0(t),t>Q\ b) i0(t), t > 0.

In the circuit in Fig. P7.21 the voltage and current expressions are v = 72e"500' V, t > 0; i = 9e~500' mA, t > 0+ . Find a) R. b) C. c) r (in milliseconds). d) the initial energy stored in the capacitor. e) how many microseconds it takes to dissipate 68% of the initial energy stored in the capacitor.

a) Use component values from Appendix H to create a first-order RC circuit (see Fig. 7.11) with a time constant of 50 ms. Use a single capacitor and a network of resistors, if necessary. Draw your circuit. b) Suppose the capacitor you chose in part (a) has an initial voltage drop of 50 V. Write an expression for the voltage drop across the capacitor for t a 0. c) Using you result from part (b), calculate the time at which the voltage drop across the capacitor has reached 10 V.

The switch in the circuit in Fig. P7.23 has been in position a for a long time and v2 0 V. At t = 0, the switch is thrown to position b. Calculate a) i, vh and v2 for t a 0+ . b) the energy stored in the capacitor at t = 0. c) the energy trapped in the circuit and the total energy dissipated in the 25 kfl resistor if the switch remains in position b indefinitely.

The switch in the circuit in Fig. P7.24 is closed at t = 0 after being open for a long time. a) Find /^0") and /2(0~). b) Find /,.(0+) andj2(0+ ). c) Explain why ^(0- ) = fj(0+ ). d) Explain why /2(0") * /2(0+ ). e) Find it(t) for t > 0. f) Find i2(t) for t > 0+ .

In the circuit shown in Fig. P7.25, both switches operate together; that is, they either open or close at the same time. The switches are closed a long time before opening at t = 0. a) How many microjoules of energy have been dissipated in the 12 kfl resistor 12 ms after the switches open? b) How long does it take to dissipate 75% of the initially stored energy?

Both switches in the circuit in Fig. P7.26 have been PSPICE closed for a long time. At t = 0, both switches open MULTISIM , . , simultaneously. a) Find ia{t) for t a ()+ . b) Find vjf) for t > 0. c) Calculate the energy (in microjoules) trapped in the circuit.

After the circuit in Fig. P7.27 has been in operation PSPICE for a long time, a screwdriver is inadvertently connected across the terminals a,b. Assume the resistance of the screwdriver is negligible. a) Find the current in the screwdriver at t = 0+ and t = co. b) Derive the expression for the current in the screwdriver for t a 0+ .

The switch in the circuit seen in Fig. P7.28 has been in position x for a long time. At t = 0, the switch moves instantaneously to position y. a) Find a so that the time constant for t > 0 is 40 ms. b) For the a found in (a), find %,

a) In Problem 7.28, how many microjoules of energy are generated by the dependent current source during the time the capacitor discharges toOV? b) Show that for t s 0 the total energy stored and generated in the capacitive circuit equals the total energy dissipated.

At the time the switch is closed in the circuit in Fig. P7.31, the voltage across the paralleled capacitors is 50 V and the voltage on the 250 nF capacitor is 40 V. a) What percentage of the initial energy stored in the three capacitors is dissipated in the 24kfl resistor? b) Repeat (a) for the 400 il and 16 kft resistors. c) What percentage of the initial energy is trapped in the capacitors?

At the time the switch is closed in the circuit shown in Fig. P7.32, the capacitors are charged as shown. a) Find v()(t) for t > 0+ . b) What percentage of the total energy initially stored in the three capacitors is dissipated in the 250 kO resistor?c) Find vx{t) for t > 0. d) Find v2(t) for t > 0. e) Find the energy (in millijoules) trapped in the ideal capacitors.

The current and voltage at the terminals of the inductor in the circuit in Fig. 7.16 are i(t) = (4 + 4 0; v(t) = -80e-40 ' V, t > 0+ . a) Specify the numerical values of Vs , JR, 7f>, and L. b) How many milliseconds after the switch has been closed does the energy stored in the inductor reach 9 J?

a) Use component values from Appendix H to create a first-order RL circuit (see Fig. 7.16) with a time constant of 8 fis. Use a single inductor and a network of resistors, if necessary. Draw your circuit. b) Suppose the inductor you chose in part (a) has no initial stored energy. At t = 0, a switch connects a voltage source with a value of 25 V in series with the inductor and equivalent resistance. Write an expression for the current through the inductor for t > 0. c) Using your result from part (b), calculate the time at which the current through the inductor reaches 75% of its final value.

The switch in the circuit shown in Fig. P7.35 has PSPICE been closed for a long time before opening at t - 0. MULTISIM a) Find the numerical expressions for iL{t) and v0(t) for f > 0. b) Find the numerical values of vL(0+ ) and v0(Q+ ).

After the switch in the circuit of Fig. P7.36 has been open for a long time, it is closed at t = 0. Calculate (a) the initial value of /; (b) the final value of /; (c) the time constant for t > 0; and (d) the numerical expression for /(/) when t & 0.

The switch in the circuit shown in Fig. P7.37 has PSPICE been in position a for a long time. At t - 0, the switch moves instantaneously to position b. a) Find the numerical expression for /(/) when t > 0. b) Find the numerical expression for v0{t) for / s 0+ .

a) Derive Eq. 7.47 by first converting the Thevenin equivalent in Fig. 7.16 to a Norton equivalent and then summing the currents away from the upper node, using the inductor voltage v as the variable of interest. b) Use the separation of variables technique to find the solution to Eq. 7.47. Verify that your solution agrees with the solution given in Eq. 7.42.

The switch in the circuit shown in Fig. P7.39 has been closed for a long time. The switch opens at t = 0. For t > 0+ : a) Find va(t) as a function of Ig, Rh R2, and L. b) Explain what happens to v0(t) as R2 gets larger and larger.c) Find vs w as a function of Ig, Rh R2, and L. d) Explain what happens to vs w as R2 gets larger and larger. Figure P7.39

The switch in the circuit in Fig. P7.41 has been PSPICE open a long time before closing at t = 0. Find vJt) MULTISIM r , ^ r>+ for t > 0 .

The switch in the circuit in Fig. P7.42 has been open a PSPICE | o n g t j m e before c i o si n g at t = 0. Find /,,(/) for / & 0.

The switch in the circuit in Fig. P7.43 has been PSPICE open a long time before closing at t = 0. Find v(>(t) MULTISIM for t a () +

There is no energy stored in the inductors L\ and L2 at the time the switch is opened in the circuit shown in Fig. P7.44. a) Derive the expressions for the currents tj(f) and i2(t) for t ^ 0. b) Use the expressions derived in (a) to find /'i(oo) and i2{oo)

The make-before-break switch in the circuit of Fig. P7.45 has been in position a for a long time. At t = 0, the switch moves instantaneously to position b. Find a) va(t), t > 0+ . b) 4(0, t c) i2(t), t 0. 0.

The switch in the circuit in Fig. P7.46 has been in PSPICE position 1 for a long time. At t = 0 it moves instanIULTISIM taneously to position 2. How many milliseconds after the switch operates does v0 equal 100 V?

For the circuit in Fig. P7.46, find (in joules): a) the total energy dissipated in the 40 ft resistor; b) the energy trapped in the inductors; c) the initial energy stored in the inductors

The current and voltage at the terminals of the capacitor in the circuit in Fig. 7.21 are /(0 = 3e-2500' mA, t > 0+ ; v(t) = (40 - 24eT25(K,0 V, t > 0. a) Specify the numerical values of Is , V0, R, C, and T. b) How many microseconds after the switch has been closed does the energy stored in the capacitor reach 81 % of its final value?

a) Use component values from Appendix H to create a first-order RC circuit (see Fig. 7.21) with a time constant of 250 ms. Use a single capacitor and a network of resistors, if necessary. Draw your circuit. b) Suppose the capacitor you chose in part (a) has an initial voltage drop of 100 V. At t = 0, a switch connects a current source with a value of 1 mA in parallel with the capacitor and equivalent resistance. Write an expression for the voltage drop across the capacitor for t 2: 0. c) Using your result from part (b), calculate the time at which the voltage drop across the capicitor reaches 50 V.

The switch in the circuit shown in Fig. P7.51 has PSPICE been closed a long time before opening at t = 0. MULHSIM For f >0 + ,find a) b) c) v0(t). aok(t). d) /2(0- e) P7.5: h(0+ ).

The switch in the circuit seen in Fig. P7.52 has been in PSPICE position a for a long time. At t = 0, the switch moves MULTISIM instantaneously to position b. For / > 0+ , find a) v0(t). b) /,,(0- c) t>g(f). d) ^(0 + ).

The circuit in Fig. P7.53 has been in operation for a PSPICE i o n g tjme. At t = 0, the voltage source reverses polarity and the current source drops from 3 mA to 2 mA. Find va(t) for t 2 0.

The switch in the circuit seen in Fig. P7.54 has been in position a for a long time. At t = 0, the switch moves instantaneously to position b. Find va(t) and i0{t) for t > 0

Assume that the switch in the circuit of Fig. P7.55 has been in position a for a long time and that at t = 0 it is moved to position b. Find (a) vc(0+ ); (b) Vc(oo); (c) rforr > 0; (d) /(0+ ); (e) vCi t > 0; and (f) i, t > 0+ .

The switch in the circuit of Fig. P7.56 has been in position a for a long time. At i = 0 the switch is moved to position b. Calculate (a) the initial voltage on the capacitor; (b) the final voltage on the capacitor; (c) the time constant (in microseconds) for t > 0; and (d) the length of time (in microseconds) required for the capacitor voltage to reach zero after the switch is moved to position b.

The switch in the circuit in Fig. P7.57 has been in PSPICE position a for a long time. At t = 0, the switch 1 moves instantaneously to position b. At the instant the switch makes contact with terminal b, switch 2 opens. Find va{t) for t a 0.

The switch in the circuit shown in Fig. P7.58 has been in the OFF position for a long time. At t = 0, the switch moves instantaneously to the ON position. Find va(t) for t >: 0.

Assume that the switch in the circuit of Fig. P7.58 PSPICE has been in the ON position for a long time before MULTISIM swit ching instantaneously to the OFF position at t = 0. Find va(t) for t > 0.

a) Derive Eq. 7.52 by first converting the Norton equivalent circuit shown in Fig. 7.21 to aThevenin equivalent and then summing the voltages around the closed loop, using the capacitor current i as the relevant variable. b) Use the separation of variables technique to find the solution to Eq. 7.52. Verify that your solution agrees with that of Eq. 7.53.

There is no energy stored in the capacitors Cx and Ci at the time the switch is closed in the circuit seen in Fig. P7.62. a) Derive the expressions for V\{t) and v2(/) for t > 0. b) Use the expressions derived in (a) to find Vi(o) and v2().

The switch in the circuit in Fig. P7.63 has been in position x for a long time. The initial charge on the 10 nF capacitor is zero. At t = 0, the switch moves instantaneously to position y. a) Find v0{t) for t > 0+ . b) Find vx{t) for t > 0.

The switch in the circuit of Fig. P7.64 has been in pspi position a for a long time. At t = 0, it moves instanWLTISIM taneous | y t o position b. For t > 0+ , find a) va(t). b) i()(t). c) Vl(t). d) v2(t). e) the energy trapped in the capacitors as t * oo

Repeat (a) and (b) in Example 7.10 if the mutual inductance is reduced to zero.

There is no energy stored in the circuit in Fig. P7.66 PSPICE at the time the switch is closed. MULTISIM a) Find /(/) for t > 0. b) Find v^t) for t > 0+ . c) Find v2(t) for t > 0. d) Do your answers make sense in terms of known circuit behavior?

Repeat Problem 7.66 if the dot on the 10 H coil is at PSPICE the top of the coil.

There is no energy stored in the circuit of Fig. P7.68 at the time the switch is closed. a) Find i0{t) for t > 0. b) Find v0(t) for t > 0+ . c) Find /, (r) for/ a 0. d) Find i2{t) for t > 0. e) Do your answers make sense in terms of known circuit behavior?

There is no energy stored in the circuit in Fig. P7.69 PSPICE at the time the switch is closed. WUTSIM a) Find ia(t) for t > 0. b) Find v0(t) for t > 0+ . c) Find i^t) for t > 0. d) Find /2(f) for t > 0. e) Do your answers make sense in terms of known circuit behavior?

The action of the two switches in the circuit seen in PSPICE Fig. P7.71 is as follows. For t < 0, switch 1 is in position a and switch 2 is open. This state has existed for a long time. At t = 0, switch 1 moves instantaneously from position a to position b, while switch 2 remains open. Ten milliseconds after switch 1 operates, switch 2 closes, remains closed for 10 ms and then opens. Find vjt) 25 ms after switch 1 moves to position b.

For the circuit in Fig. P7.71, how many milliseconds after switch 1 moves to position b is the energy stored in the inductor 4% of its initial value?

The switch in the circuit shown in Fig. P7.73 has been in position a for a long time. At t = 0, the switch is moved to position b, where it remains for 1 ms. The switch is then moved to position c, where it remains indefinitely. Find a) /(0+ ). b) /(200/AS). c) /(6 ms). d) -y(l"ms). e) -y(l+ms).

There is no energy stored in the capacitor in the cirPSPICE cu it in Fig. P7.74 when switch 1 closes at t = 0. Ten microseconds later, switch 2 closes. Find va{t) for t > 0. Figure P7.74 r^rrA 16 kfl 30 V

The capacitor in the circuit seen in Fig. P7.75 has PSPICE been charged to 300 V. At t = 0, switch 1 closes, causing the capacitor to discharge into the resistive network. Switch 2 closes 200/ts after switch 1 closes. Find the magnitude and direction of the current in the second switch 300 /AS after switch 1 closes. Figure P7.75 60 kfl 300 V 40 kfl

In the circuit in Fig. P7.76, switch 1 has been in position a and switch 2 has been closed for a long time. At t = 0, switch 1 moves instantaneously to position b. Eight hundred microseconds later, switch 2 opens, remains open for 300 tts, and then recloses. Find va 1.5 ms after switch 1 makes contact with terminal b.

For the circuit in Fig. P7.76, what percentage of the PSPICE initial energy stored in the 500 nF capacitor is dissiMumsiM pated in the 3 kfl resistor?

The switch in the circuit in Fig. P7.78 has been in PSPICE position a for a long time. Alt = 0, it moves instantaneously to position b, where it remains for five seconds before moving instantaneously to position c. Find va for t ^ 0.

The voltage waveform shown in Fig. P7.79(a) is PSPICE applied to the circuit of Fig. P7.79(b). The initial mTISIM current in the inductor is zero. a) Calculate v( ,(t). b) Make a sketch of v0(t) versus t. c) Find i() at t = 5 ms. Figure P7.79 %(V) 80 20 fl !40mH v, 2.5 t (ms) (a) (b)

The voltage waveform shown in Fig. P7.81(a) is PSPICE applied to the circuit of Fig. P7.81 (b). The initial voltage on the capacitor is zero. a) Calculate v0{t). b) Make a sketch of v()(t) versus t.

The voltage signal source in the circuit in Fig. P7.82(a) PSPICE is generating the signal shown in Fig. P7.82(b).There is mnm no stored energy at f = 0. a) Derive the expressions for v0{t) that apply in the intervals t < 0; 0 < t < 4 ms; 4 ms < t < 8 ms; and 8 ms < t < oo. b) Sketch va and vs on the same coordinate axes. c) Repeat (a) and (b) with R reduced to 50 kfi.

The current source in the circuit in Fig. P7.83(a) PSPICE generates the current pulse shown in Fig. P7.83(b). mnsiM Ther e i s Q O energ y store d a t t = Q a) Derive the expressions for i0(t) and v0(t) for the time intervals /<r< 2 ms; and 2 ms < t < oo. b) Calculate io(0~); io(0+ ); /o(0.002"); and /;/0.002+ ). c) Calculate vQ(0~); vo(0+ ); t?o(0.002~); and ^(0.002+ ).d) Sketch ia{t) versus t for the interval - 1 ms < t < 4 ms. e) Sketch va(t) versus t for the interval - 1 ms < t < 4 ms.

The capacitor in the circuit shown in Fig. P7.84 is PSPICE charged to 20 V at the time the switch is closed. If the capacitor ruptures when its terminal voltage equals or exceeds 20 kV, how long does it take to rupture the capacitor?

The switch in the circuit in Fig. P7.85 has been PSPICE closed for a long time. The maximum voltage rating mns,M of the 1.6 ^ F capacitor is 14.4 kV. How long after the switch is opened does the voltage across the capacitor reach the maximum voltage rating?

The inductor current in the circuit in Fig. P7.86 is 25 mA at the instant the switch is opened. The inductor will malfunction whenever the magnitude of the inductor current equals or exceeds 5 A. How long after the switch is opened does the inductor malfunction?

The gap in the circuit seen in Fig. P7.87 will arc over PSPICE whenever the voltage across the gap reaches 45 kV. The initial current in the inductor is zero. The value of /3 is adjusted so the Thevenin resistance with respect to the terminals of the inductor is 5 kO. a) What is the value of /3? b) How many microseconds after the switch has been closed will the gap arc over?

The circuit shown in Fig. P7.88 is used to close the switch between a and b for a predetermined length of time. The electric relay holds its contact arms down as long as the voltage across the relay coil exceeds 5 V. When the coil voltage equals 5 V, the relay contacts return to their initial position by a mechanical spring action. The switch between a and b is initially closed by momentarily pressing the push button. Assume that the capacitor is fully charged when the push button is first pushed down. The resistance of the relay coil is 25 kO, and the inductance of the coil is negligible. a) How long will the switch between a and b remain closed? b) Write the numerical expression for i from the time the relay contacts first open to the time the capacitor is completely charged. c) How many milliseconds (after the circuit between a and b is interrupted) does it take the capacitor to reach 85% of its final value?

The voltage pulse shown in Fig. P7.89(a) is applied PSPICE to the ideal integrating amplifier shown in Fig. P7.89(b). Derive the numerical expressions for v(>(t) when vo(0) = 0 for the time intervals a) t < 0. b) 0 < t < 250 ms. c) 250 ms < t < 500 ms. d) 500 ms < t < oo. Figure P7.89 vg (mV) 200 0 -200 250 500 t(ms)

The energy stored in the capacitor in the circuit PSPICE shown in Fig. P7.91 is zero at the instant the switch is closed. The ideal operational amplifier reaches saturation in 15 ms. What is the numerical value of R in kilo-ohms?

At the instant the switch is closed in the circuit of PSPICE Fig. P7.91, the capacitor is charged to 6 V, positive at HULTISIM th e right-hand terminal. If the ideal operational amplifier saturates in 40 ms, what is the value of /??

The voltage source in the circuit in Fig. P7.93(a) is PSPICE generating the triangular waveform shown in MULTISIM Fi g P 7 93 ( b ) Assume the energy stored in the capacitor is zero at t = 0 and the op amp is ideal. a) Derive the numerical expressions for va{t) for the following time intervals: 0 < t < 1 /xs; 1 /xs < / < 3 /xs; and 3 /xs ^ t ^ 4 /xs. b) Sketch the output waveform between 0 and 4 /xs. c) If the triangular input voltage continues to repeat itself for t > 4 /xs, what would you expect the output voltage to be? Explain.

There is no energy stored in the capacitors in the PSPICE c ircu it shown in Fig. P7.94 at the instant the two MULTISIM . , , i , switches close. Assume the op amp is ideal. a) Find v() as a function of v&, vb, R, and C. b) On the basis of the result obtained in (a), describe the operation of the circuit. c) How long will it take to saturate the amplifier if va = 40 mV; vh = 15mV; R = 50 kO; C = 10 nF; and Vcc = 6 V?

At the time the double-pole switch in the circuit PSPICE shown in Fig. P7.95 is closed, the initial voltages on MULTISIM . . -rti r . AVT I T - I t the capacitors are 12 V and 4 V, as shown. Find the numerical expressions for vt>(t), v2(t), and vAt) that are applicable as long as the ideal op amp operates in its linear range.

At the instant the switch of Fig. P7.96 is closed, the PSPKE voltage on the capacitor is 56 V. Assume an ideal operational amplifier. How many milliseconds after the switch is closed will the output voltage v equal zero?

The circuit shown in Fig. P7.97 is known as a monostable multivibrator.The adjective monostable is used to describe the fact that the circuit has one stable state. That is, if left alone, the electronic switch T2 will be ON, and Tj will be OFF. (The operation of the ideal transistor switch is described in detail in Problem 7.99.) T2 can be turned OFF by momentarily closing the switch S. After S returns to its open position, T2 will return to its ON state. a) Show that if T2 is ON, T{ is OFF and will stay OFF. b) Explain why T2 is turned OFF when S is momentarily closed. c) Show that T2 will stay OFF for RC In 2 s.

The parameter values in the circuit in Fig. P7.97 are Vcc = 6 V; Rx = 5.0 kft; RL = 20 kH; C = 250 pF; and R = 23,083 H. a) Sketch vce2 versus t, assuming that after S is momentarily closed, it remains open until the circuit has reached its stable state. Assume S is closed at t = 0. Make your sketch for the interval - 5 < t < lOjus. b) Repeat (a) for /b2 versus t.

PSPICE MULTISIM The circuit shown in Fig. P7.99 is known as an astable multivibrator and finds wide application in pulse circuits. The purpose of this problem is to relate the charging and discharging of the capacitors to the operation of the circuit. The key to analyzing the circuit is to understand the behavior of the ideal transistor switches Ti and T2. The circuit is designed so that the switches automatically alternate between ON and OFF. When T{ is OFF, T2 is ON and vice versa. Thus in the analysis of this circuit, we assume a switch is either ON or OFF. We also assume that the ideal transistor switch can change its state instantaneously. In other words, it can snap from OFF to ON and vice versa. When a transistor switch is ON, (1) the base current ib is greater than zero, (2) the terminal voltage vbc is zero, and (3) the terminal voltage vce is zero. Thus, when a transistor switch is ON, it presents a short circuit between the terminals b,e and c,e. When a transistor switch is OFF, (1) the terminal voltage vhe is negative, (2) the base current is zero, and (3) there is an open circuit between the terminals c,e. Thus when a transistor switch is OFF, it presents an open circuit between the terminals b,e and c,e. Assume that T2 has been ON and has just snapped OFF, while Tj has been OFF and has just snapped ON. You may assume that at this instance, C2 is charged to the supply voltage Vcc, an d tn e charge on C\ is zero. Also assume Cx = C2 and Rx = R2 = 10RL. a) Derive the expression for vbc2 during the interval that T2 is OFF. b) Derive the expression for vcc2 during the interval that T2 is OFF. c) Find the length of time T2 is OFF. d) Find the value of vce2 at the end of the interval that T2 is OFF. e) Derive the expression for /bl during the interval that T2 is OFF. f) Find the value of ibx at the end of the interval that T2 is OFF. g) Sketch vcc2 versus t during the interval that T2 is OFF. h) Sketch /M versus t during the interval that T2 is OFF.

Repeat Problem 7.100 with C{ = 3 nF and C2 = 2.8 nF. All other component values are unchanged.

The astable multivibrator circuit in Fig. P7.99 is to satisfy the following criteria: (1) One transistor switch is to be ON for 48 /AS and OFF for 36 (xs for each cycle; (2) RL = 2 kH; (3) Vcc = 5 V; (4) R\ = R2\ and (5) 6RL < R^ ^ 50RL. What are the limiting values for the capacitors C\ and C2?

Suppose the circuit in Fig. 7.45 models a portable PRACTICAL flashing light circuit. Assume that four 1.5 V batteries power the circuit, and that the capacitor value is 10 /JLF. Assume that the lamp conducts when its voltage reaches 4 V and stops conducting when its voltage drops below 1 V. The lamp has a resistance of 20 kO when it is conducting and has an infinite resistance when it is not conducting. a) Suppose we don't want to wait more than 10 s in between flashes. What value of resistance R is required to meet this time constraint? b) For the value of resistance from (a), how long does the flash of light last?

In the circuit of Fig. 7.45, the lamp starts to conduct PRACTICAL whenever the lamp voltage reaches 15 V. During PERSPECTIVE r O & the time when the lamp conducts, it can be modeled as a 10 kfl resistor. Once the lamp conducts, it will continue to conduct until the lamp voltage drops to 5 V. When the lamp is not conducting, it appears as an open circuit. Vs = 40 V; R - 800 kO; and C = 25 fiF. a) How many times per minute will the lamp turn on? b) The 800 kfl resistor is replaced with a variable resistor R. The resistance is adjusted until the lamp flashes 12 times per minute. What is the value of /??

In the flashing light circuit shown in Fig. 7.45, the PRACTICAL lamp can be modeled as a 1.3 kO resistor when it is PERSPECTIVE r PSPICE conducting. The lamp triggers at 900 V and cuts off MULTISIM at 30 0 V. a) If Vs = 1000 V, R = 3.7 kO, and C = 250 fiF, how many times per minute will the light flash? b) What is the average current in milliamps delivered by the source? c) Assume the flashing light is operated 24 hours per day. If the cost of power is 5 cents per kilowatthour, how much does it cost to operate the light per year?

a) Show that the expression for the voltage drop across the capacitor while the lamp is conducting in the flashing light circuit in Fig. 7.48 is given by vL(0 = Vm + (Vmax - VTh)t'-<'-"^ PRACTICAL PERSPECTIVE where Vi R> Th v; R + RL RRLC 7 R + RL' b) Show that the expression for the time the lamp conducts in the flashing light circuit in Fig. 7.48 is given by (tc ~ Q RRLc , V U - vTh R + R, In v K, ih

Th e rela y show n i n Fig . P7.10 7 connect s th e 3 0 V dc PRACTICAL generato r t o th e d c bu s a s lon g a s th e rela y current PERSPECTIV E b & J is greater than 0.4 A. If the relay current drop s to 0. 4 A o r less , th e spring-loade d rela y immediately connect s th e d c bu s t o th e 3 0 V standb y battery . The resistanc e o f th e rela y windin g i s 6 0 ft. Th e induc - tanc e o f th e rela y windin g i s t o b e determined. a ) Assum e th e prim e moto r drivin g th e 3 0 V dc generato r abruptl y slow s down , causin g th e gen - erate d voltag e t o dro p suddenl y t o 2 1 V . What valu e o f L wil l assur e tha t th e standb y battery wil l b e connecte d t o th e d c bu s i n 0. 5 seconds? b ) Usin g th e valu e o f L determine d i n (a) , state ho w lon g i t wil l tak e th e rela y t o operat e if the generate d voltag e suddenl y drop s t o zero. Figure P7.107 30 V r v , *en ^ (R,L) DC