Electric Circuits 9th Edition solutions

Electric Circuits 9
Find the phasor transform of each trigonometric function: a) v = 170cos(377r - 40) V. b) i = 10 sin (1000/1 + 20) A. c) i = [5 cos (art + 36.87) + 10cos(art -53.13)] A. d) v = [300cos(20,00077t + 45) - 100 sin(20,0007rr + 30)] mV.

Electric Circuits 9
Find the time-domain expression corresponding to each phasor: a) V = 18.6/-54 V. b) I = (20/45^ - 50/-30) mA. c) V = (20 + /80 - 30/15) V.

Electric Circuits 9
The current in the 20 mH inductor is 10 cos (10,000? + 30) mA. Calculate (a) the inductive reactance; (b) the impedance of the inductor; (c) the phasor voltage V; and (d) the steady-state expression for v(t). 20 mH

Electric Circuits 9
The current in the 20 mH inductor is 10 cos (10,000? + 30) mA. Calculate (a) the inductive reactance; (b) the impedance of the inductor; (c) the phasor voltage V; and (d) the steady-state expression for v(t). 20 mH

Electric Circuits 9
Four branches terminate at a common node. The reference direction of each branch current (*j, i2, /3, and /4) is toward the node. If NOTE: Also try Chapter Problem 9.15. ix = 100 cos (G>* + 25) A, i2 = 100cos(o)f + 145) A, and 13 = 100 cos (eat - 95) A, find/4.

Electric Circuits 9
Using the values of resistance and inductance in the circuit of Fig. 9.15, let Ys = 125 /-60 V and a) = 5000 rad/s. Find a) the value of capacitance that yields a steady-state output current i with a phase angle of -105. b) the magnitude of the steady-state output current f

Electric Circuits 9
A 20 fl resistor is connected in parallel with a 5 mH inductor. This parallel combination is connected in series with a 5 ft resistor and a 25 ^iF capacitor. a) Calculate the impedance of this interconnection if the frequency is 2 krad/s. b) Repeat (a) for a frequency of 8 krad/s. c) At what finite f

Electric Circuits 9
The interconnection described in Assessment Problem 9.7 is connected across the terminals of a voltage source that is generating v = 150 cos 4000f V. What is the maximum amplitude of the current in the 5 mH inductor?

Electric Circuits 9
Use a A -to-Y transformation to find the current I in the circuit shown.

Electric Circuits 9
Find the Thevenin equivalent with respect to terminals a,b in the circuit shown.

Electric Circuits 9
Use the node-voltage method to find the steadystate expression for v(t) in the circuit shown. The sinusoidal sources are is = 10 cos cot A and vs = 100 sin cot V, where to - 50 krad/s.

Electric Circuits 9
Use the mesh-current method to find the phasor current I in the circuit shown.

Electric Circuits 9
A linear transformer couples a load consisting of a 360 O resistor in series with a 0.25 H inductor to a sinusoidal voltage source, as shown. The voltage source has an internal impedance of 184 + /0 Cl and a maximum voltage of 245.20 V, and it is operating at 800 rad/s. The transformer parameters are

Electric Circuits 9
The source voltage in the phasor domain circuit in the accompanying figure is 25 /0 kV. Find the amplitude and phase angle of V2 an d ^2-

Electric Circuits 9
A 10 O resistor and a 5 /xF capacitor are connected PSPICE i n parallel. This parallel combination is also in par1 allel with the series combination of an 8 O resistor and a 300 /xH inductor. These three parallel branches are driven by a sinusoidal current source whose current is 922 cos(20,000r + 30

Electric Circuits 9
a) Show that, at a given frequency w, the circuits in Fig. P9.17(a) and (b) will have the same impedance between the terminals a,b if 2 J 2 /e, - a>z LjR2 R\ + co 2 L 2 2 U Rl^i R\ + (o2 L\ b) Find the values of resistance and inductance that when connected in series will have the same impedance at 4

Electric Circuits 9
a) Show that at a given frequency eo, the circuits in Fig. P9.17(a) and (b) will have the same impedance between the terminals a,b if Ro = R] + a?L\ u = R\ + o)2 L\ 2f (Hint: The two circuits will have the same impedance if they have the same admittance.) b) Find the values of resistance and inductan

Electric Circuits 9
a) Show that at a given frequency to, the circuits in Fig. P9.19(a) and (b) will have the same impedance between the terminals a,b if /?i = Q = R2 1 + o?R\c\ 1 + arRJCJ w 2RJC2 b) Find the values of resistance and capacitance that when connected in series will have the same impedance at 40 krad/s as

Electric Circuits 9
a) Using component values from Appendix H, combine at least one resistor, inductor, and capacitor in series to create an impedance of 300 - /400 ft at a frequency of 10,000 rad/s. b) At what frequency does the circuit from part (a) have an impedance that is purely resistive?

Electric Circuits 9
a) Using component values from Appendix H, combine at least one resistor and one inductor in parallel to create an impedance of 40 + /20 ft at a frequency of 5000 rad/s. (HintUse the results of Problem 9.18.)b) Using component values from Appendix H, combine at least one resistor and one capacitor in

Electric Circuits 9
a) Using component values from Appendix H, find a single capacitor or a network of capacitors that, when combined in parallel with the RL circuit from Problem 9.22(a), gives an equivalent impedance that is purely resistive at a frequency of 5000 rad/s. b) Using component values from Appendix H, find

Electric Circuits 9
Three branches having impedances of 3 + /4 O, 16 - /12 ft, and -/ 4 ft, respectively, are connected in parallel. What are the equivalent (a) admittance, (b) conductance, and (c) susceptance of the parallel connection in millisiemens? (d) If the parallel branches are excited from a sinusoidal current

Electric Circuits 9
a) For the circuit shown in Fig. P9.25, find the frePSPICE quency (in radians per second) at which the impedance Zab is purely resistive, b) Find the value of Za b at the frequency of (a).

Electric Circuits 9
Find the admittance K,b in the circuit seen in Fig. P9.26. Express K(lb in both polar and rectangular form. Give the value of Yab in millisiemens.

Electric Circuits 9
Find the impedance Zab in the circuit seen in Fig. P9.27. Express Za b in both polar and rectangular form.

Electric Circuits 9
The circuit shown in Fig. P9.28 is operating in the sinusoidal steady state. Find the value of co if i(} = 40 sin (a)/ + 21.87) mA. vg = 40cos(o>/ - 15) V.

Electric Circuits 9
The circuit in Fig. P9.29 is operating in the sinuPSPICE soidal steady state. Find the steady-state expression M"LTISIM f orVw (f )i f u = 40 cos 50,000/ V.

Electric Circuits 9
Find the steady-state expression for /(/) in the circuit in Fig. P9.31 if vs = 100 sin 50/ mV.

Electric Circuits 9
Find the steady-state expression for v(> in the circuit of Fig. P9.32 if ig = 500 cos 2000/ m A.

Electric Circuits 9
The phasor current Ia in the circuit shown in PSPICE Fig. P9.33 is 2/0 A. lumsiM a) Find Ib, Ic, and Vg. b) If a) = 800 rad/s, write the expressions for ib(t), /c(/), and vM).

Electric Circuits 9
The circuit in Fig. P9.34 is operating in the sinusoidal PSPICE steady state. Find v0(t) if /,(/) = 3 cos 200/ mA.

Electric Circuits 9
Find the value of Z in the circuit seen in Fig. P9.35 if Vg = 100 - /50 V, I g = 30 + /20 A, and \i = 140 + /30 V.

Electric Circuits 9
Find Ib and Z in the circuit shown in Fig. P9.36 if VJJ = 25/(T V and I a = 5 /90 A.

Electric Circuits 9
Find Zab for the circuit shown in Fig P9.37.

Electric Circuits 9
a) The frequency of the source voltage in the circuit in Fig. P9.38 is adjusted until ig is in phase with Vr What is the value of co in radians per second? b) If vg = 20 cos a)t V (where a> is the frequency found in [a]), what is the steady-state expression for vnl

Electric Circuits 9
The frequency of the sinusoidal voltage source in PSPICE the circuit in Fig. P9.39 is adjusted until the current "1ULTISIM i ;._ ia is in phase with vg. a) Find the frequency in hertz. b) Find the steady-state expression for ig (at the frequency found in [a]) if vg = 30 cos wt V.

Electric Circuits 9
a) The source voltage in the circuit in Fig. P9.41 is Vg - 50 cos 50,000f V. Find the values of L such that ig is in phase with vg when the circuit is operating in the steady state. b) For the values of L found in (a), find the steadystate expressions for ig.

Electric Circuits 9
The frequency of the sinusoidal current source in PSPICE the circuit in Fig. P9.42 is adjusted until va is in mTISIM phase with ir a) What is the value of a) in radians per second? b) If ig = 2.5 cos oit mA (where to is the frequency found in [a]), what is the steady-state expression for u,?

Electric Circuits 9
The device in Fig. P9.43 is represented in the frequency domain by a Norton equivalent. When a resistor having an impedance of 5 kft is connected across the device, the value of V0 is 5 /15 V. When a capacitor having an impedance of -/ 3 kft is connected across the device, the value of I() is 4.5 -

Electric Circuits 9
The sinusoidal voltage source in the circuit in Fig. P9.44 is developing a voltage equal to 247.49 cos (lOOOf+ 45) V. a) Find the Thevenin voltage with respect to the terminals a,b. b) Find the Thevenin impedance with respect to the terminals a,b. c) Draw the Thevenin equivalent.

Electric Circuits 9
Use source transformations to find the Thevenin equivalent circuit with respect to the terminals a,b for the circuit shown in Fig. P9.45.

Electric Circuits 9
Use source transformations to find the Norton equivalent circuit with respect to the terminals a,b for the circuit shown in Fie. P9.46.

Electric Circuits 9
Find the Thevenin equivalent circuit with respect to the terminals a,b for the circuit shown in Fig. P9.47

Electric Circuits 9
Find the Thevenin equivalent circuit with respect to the terminals a,b of the circuit shown in Fig. P9.48.

Electric Circuits 9
Find the Norton equivalent with respect to terminals a,b in the circuit of Fig. P9.49.

Electric Circuits 9
Find the Thevenin impedance seen looking into the terminals a,b of the circuit in Fig. P9.51 if the frequency of operation is (25/TT) kHz.

Electric Circuits 9
Find the Norton equivalent circuit with respect to the terminals a,b for the circuit shown in Fig. P9.52 whenVy = 5/0 V.

Electric Circuits 9
The circuit shown in Fig. P9.53 is operating at a frequency of 10 rad/s. Assume a is real and lies between -10 and +10, that is, -10 < a < 10. a) Find the value of a so that the Thevenin impedance looking into the terminals a,b is purely resistive. b) What is the value of the Thevenin impedance for t

Electric Circuits 9
Use the node-voltage method to find the steadyPSPICE state expression for v()(t) in the circuit in Fig. P9.54 if MULTISIM % = 20cos(2000r - 36.87) V,vg2 = 50sin(2000r - 16.26) V.

Electric Circuits 9
Use the node-voltage method to find \(> in the circuit in Fig. P9.55.

Electric Circuits 9
Use the node-voltage method to find the phasor voltage V in the circuit shown in Fig. P9.56.

Electric Circuits 9
Use the node voltage method to find the steady-state PSPICE expressions for the branch currents /a, ib, and /c in the MULTISIM circuit seen in Fig. P9.57 if v& = 50sinl0fVV and Vb = 25 cos (106 / + 90) V.

Electric Circuits 9
Us e the node-voltage method to find Vf) and I in the circuit seen in Fig. P9.58.

Electric Circuits 9
Us e the node-voltage method to find the phasor voltage V in the circuit shown in Fig. P9.59. Express the voltage in both polar and rectangular form.

Electric Circuits 9
Us e the mesh-current method to find the steadystate expression for i(){t) in the circuit in Fig. P9.61 if va = 60 cos 40,000/ V, vh = 90 sin (40,000* + 180) V.

Electric Circuits 9
Us e the mesh-current method to find the phasor current lg in the circuit in Fig. P9.56.

Electric Circuits 9
Us e the mesh-current method to find the branch currents I. I h , I c , and I d in the circuit shown in Fig. P9.63.

Electric Circuits 9
Use the mesh-current method to find the steadyPSPICE s tat e expression for va in the circuit seen in " " Fig< p9. 6 4 if v equa | s \ 3 0 CO s 10,000/ V.

Electric Circuits 9
Use the concept of current division to find the PSPICE steady-state expression for i(> in the circuit in Mum pig. P9.65 if/^ = 125 cos 12,500* mA.

Electric Circuits 9
Use the concept of voltage division to find the PSPICE steady-state expression for v()(t) in the circuit in LTISIM Fi g p 9 6 6 i f v = 7 5 co s 20,000/ V.

Electric Circuits 9
The op amp in the circuit seen in Fig. P9.67 is ideal. PSPICE Find the steady-state expression for v(>(t) when - =2cosl(/Y V

Electric Circuits 9
The op amp in the circuit in Fig. P9.68 is ideal. MULTISIM a ) ^ n

Electric Circuits 9
The sinusoidal voltage source in the circuit shown in PSPICE pig P9.69 is generating the voltage v = 4 cos 200r V. MULTISIM ..11,- 1 i If the op amp is ideal, what is the steady-state expression for v0(t)1

Electric Circuits 9
The operational amplifier in the circuit shown in PSPICE Fig. P9.71 is ideal. The voltage of the ideal sinuMULTISIM , 1 . ir i r\f\* t / soida 1 source is vg = 30 cos 10t V. a) How small can Ca be before the steady-state output voltage no longer has a pure sinusoidal waveform? b) For the value of C

Electric Circuits 9
a) Find the input impedance Zab for the circuit in Fig. P9.72. Express Zab as a function of Z and K where K = (R2/R\). b) If Z is a pure capacitive element, what is the capacitance seen looking into the terminals a,b?

Electric Circuits 9
For the circuit in Fig. P9.73 suppose vt = 20 cos(2000f - 36.87) V v2 = 10cos(5000/ + 16.26) V a) What circuit analysis technique must be used to find the steady-state expression for vv(t)1 b) Find the steady-state expression for vC)(t).

Electric Circuits 9
For the circuit in Fig. P9.61, suppose v.d = 5 cos 80,000/ V vb = -2.5 cos 320,000/ V. b) Find the coefficient of coupling. c) Find the energy stored in the magnetically coupled coils at t = 1007T /xs and t = 200-7T ^s. Figure P9.77 30 a a) What circuit analysis technique must be used to find the ste

Electric Circuits 9
A series combination of a 300 O resistor and a 100 m H inductor is connected to a sinusoidal voltage source by a linear transformer. The source is operating at a frequency of 1 krad/s. A t this frequency, the internal impedance of the source is 100 + /13.74 CI. The rms voltage at the terminals of the

Electric Circuits 9
The sinusoidal voltage source in the circuit seen in PSPICE Fig. P9.76 is operating at a frequency of 200 krad/s. LTISIM ^ e coe ff}c j etl t 0 f coupling is adjusted until the peak amplitude of ix is maximum. a) What is the value of kl b) What is the peak amplitude of /j if vg = 560 cos(2 X 10 V ?

Electric Circuits 9
a) Find the steady-state expressions for the currents ig and iL in the circuit in Fig. P9.77 when PSPICE MU LTISIM vg = 70 cos 5000/ V.b) Find the coefficient of coupling. c) Find the energy stored in the magnetically coupled coils at t = 1007T /xs and t = 200-7T ^s.

Electric Circuits 9
For the circuit in Fig. P9.78, find the Thevenin equivalent with respect to the terminals c,d.

Electric Circuits 9
The value of k in the circuit in Fig. P9.79 is adjusted so that Za b is purely resistive when a> = 4 krad/s. Find Zab.

Electric Circuits 9
a) Show that the impedanc e seen looking into the terminals a,b in the circuit in Fig. P9.81 on the next page is given by the expression b) Show that if the polarity terminals of either one of the coils is reversed,

Electric Circuits 9
a) Show that the impedance seen looking into the terminals a,b in the circuit in Fig. P9.82 is given by the expression Zab - ZL 1 + N-, b) Show that if the polarity terminal of either one of the coils is reversed that

Electric Circuits 9
Find the impedance Za b in the circuit in Fig. P9.83 if ZL = 80/60'H .

Electric Circuits 9
Show by using a phasor diagram what happens to PSPICE the magnitude and phase angle of the voltage v in MULTISIM th e circui t i n Fi g p 9 8 4 a s R^ j s yaric d fro m zer o t Q infinity. The amplitude and phase angle of the source voltage are held constant as Rx varies

Electric Circuits 9
The parameters in the circuit shown in Fig. 9.53 are /?, = 0.1 il,o)Lx = 0.8 ft,fl2 = 24 il,(oL2 = 32 ft, and VL = 240 + / 0 V. a) Calculate the phasor voltage Vs . b) Connect a capacitor in parallel with the inductor, hold VL constant, and adjust the capacitor until the magnitude of I is a minimum.

Electric Circuits 9
a) For the circuit shown in Fig. P9.86, compute Vv and V/. b) Construct a phasor diagram showing the relationship between Vs , V/, and the load voltage of 240/0 V. c) Repeat parts (a) and (b), given that the load voltage remains constant at 240 /0 V, when a capacitive reactance of - 5 Cl is connect

Electric Circuits 9
You may have the opportunity as an engineering graduate to serve as an expert witness in lawsuits involving either personal injury or property damage. As an example of the type of problem on which you may be asked to give an opinion, consider the following event. At the end of a day of fieldwork, a f

Electric Circuits 9
a) Calculate the branch currents I]-I

Electric Circuits 9
Suppose the 40 ft resistance in the distribution cirpRAcncAL cuit in Fie. 9.58 is replaced bv a 20 ft resistance. PERSPECTIVE r a) Recalculate the branch current in the 2 (1 resistor, I2. b) Recalculate the primary current, Ip. c) On the basis of your answers, is it desirable to have the resistance o

Electric Circuits 9
a) Find the primary current I p for (c) and (d) in P nwr PRACTICAL Problem 9.90. K m moa n PERSPECTIVE Fuse B( 100 A) b) Do your answers make sense in terms of known circuit behavior?