(a) For two inductors in series as in Fig. 6.81(a), show

If the voltage across a 7.5-F capacitor is 2te3t V, find the current and the power.

A capacitor has energy w(t) 10 cos2 50-mF 377t J. Determine the current through the capacitor.

Design a problem to help other students better understand how capacitors work.

A current of A flows through a 5-F capacitor. Find the voltage across the capacitor given that v(0) 1 V.

The voltage across a capacitor is shown in Fig. 6.45. Find the current waveform.

The voltage waveform in Fig. 6.46 is applied across a capacitor. Draw the current waveform through it.

At , the voltage across a 25-mF capacitor is 10 V. Calculate the voltage across the capacitor for when current 5t mA flows through it.

A 4-mF capacitor has the terminal voltage If the capacitor has an initial current of 2 A, find: (a) the constants A and B, (b) the energy stored in the capacitor at (c) the capacitor current for t 7 0.

The current through a 0.5-F capacitor is 6(1 et ) A. Determine the voltage and power at Assume v(0) 0.

The voltage across a 5-mF capacitor is shown in Fig. 6.47. Determine the current through the capacitor.

A 4-mF capacitor has the current waveform shown in Fig. 6.48. Assuming that sketch the voltage waveform v(t). v(0)

A voltage of appears across a parallel combination of a 100-mF capacitor and a resistor. Calculate the power absorbed by the parallel combination

Find the voltage across the capacitors in the circuit of Fig. 6.49 under dc conditions.

Series-connected 20-pF and 60-pF capacitors are placed in parallel with series-connected 30-pF and 70-pF capacitors. Determine the equivalent capacitance.

Two capacitors ( and ) are connected to a 100-V source. Find the energy stored in each capacitor if they are connected in: (a) parallel (b) series

The equivalent capacitance at terminals a-b in the circuit of Fig. 6.50 is Calculate the value of 30 mF. C.

Determine the equivalent capacitance for each of the circuits of Fig. 6.51.

Find in the circuit of Fig. 6.52 if all capacitors are 4 mF.

Find the equivalent capacitance between terminals a and b in the circuit of Fig. 6.53. All capacitances are in mF.

Find the equivalent capacitance at terminals a-b of the circuit in Fig. 6.54.

Determine the equivalent capacitance at terminals a-b of the circuit in Fig. 6.55.

Obtain the equivalent capacitance of the circuit in Fig. 6.56.

Using Fig. 6.57, design a problem that will help other students better understand how capacitors work together when connected in series and in parallel.

For the circuit in Figure 6.58, determine (a) the voltage across each capacitor and (b) the energy stored in each capacitor.

(a) Show that the voltage-division rule for two capacitors in series as in Fig. 6.59(a) is assuming that the initial conditions are zero. v1 C2 C1 C2 vs, v2 C1 C1 C2 vs (b) For two capacitors in parallel as in Fig. 6.59(b), show that the current-division rule is assuming that the initial conditions are zero

Three capacitors, C1 5 mF, C2 10 mF, and C3 20 mF, are connected in parallel across a 150-V source. Determine: (a) the total capacitance, (b) the charge on each capacitor, (c) the total energy stored in the parallel combination

Given that four capacitors can be connected in series and in parallel, find the minimum and maximum values that can be obtained by such series/parallel combinations.

Obtain the equivalent capacitance of the network shown in Fig. 6.60.

Determine for each circuit in Fig. 6.61.

Assuming that the capacitors are initially uncharged, find in the circuit of Fig. 6.62.

If find and in the circuit of Fig. 6.63. i2 v(t), i (t) 1 v(0) 0,

In the circuit of Fig. 6.64, let is 50e2t mA and v (t) 1(0) 50 V, v2(0) 20 V. Determine: v (t) 1(0) 50 V, v2(0) 20 V.

Obtain the Thevenin equivalent at the terminals, a-b, of the circuit shown in Fig. 6.65. Please note that Thevenin equivalent circuits do not generally exist for circuits involving capacitors and resistors. This is a special case where the Thevenin equivalent circuit does exist.

The current through a 10-mH inductor is 10et2 A. Find the voltage and the power at t 3 s.

An inductor has a linear change in current from 50 mA to 100 mA in 2 ms and induces a voltage of 160 mV. Calculate the value of the inductor.

Design a problem to help other students better understand how inductors work.

The current through a 12-mH inductor is 4 sin 100t A. Find the voltage, across the inductor for 0 6 t 6 p200 s, and the energy stored at t p 200.

The current through a 40-mH inductor is i(t) b 0, t 6 0 te2t A, t 7 0 Find the voltage v(t).

The voltage across a 200-mH inductor is given by v(t) 3t 2 2t 4 V for t 7 0. Determine the current through the inductor. Assume that i(0) 1 A.

The current through a 5-mH inductor is shown in Fig. 6.66. Determine the voltage across the inductor at and 5 ms.

The voltage across a 2-H inductor is 20(1 e2t ) V. If the initial current through the inductor is 0.3 A, find the current and the energy stored in the inductor at t 1 s.

If the voltage waveform in Fig. 6.67 is applied across the terminals of a 5-H inductor, calculate the current through the inductor. Assume i(0) 1 A.

The current in an 80-mH inductor increases from 0 to 60 mA. How much energy is stored in the inductor?

A 100-mH inductor is connected in parallel with a 2-k resistor. The current through the inductor is i(t) 50e vL 400t mA. (a) Find the voltage across the inductor. (b) Find the voltage across the resistor. (c) Does vR(t) vL(t) 0? (d) Calculate the energy in the inductor at t 0.

If the voltage waveform in Fig. 6.68 is applied to a 10-mH inductor, find the inductor current Assume i(0) 0.

Find and the energy stored in the capacitor and inductor in the circuit of Fig. 6.69 under dc conditions.

For the circuit in Fig. 6.70, calculate the value of R that will make the energy stored in the capacitor the same as that stored in the inductor under dc conditions.

Under steady-state dc conditions, find i and in the circuit in Fig. 6.71.

Find the equivalent inductance of the circuit in Fig. 6.72. Assume all inductors are 10 mH.

An energy-storage network consists of seriesconnected 16-mH and 14-mH inductors in parallel with series-connected 24-mH and 36-mH inductors. Calculate the equivalent inductance.

Determine at terminals a-b of the circuit in Fig. 6.73.

Using Fig. 6.74, design a problem to help other students better understand how inductors behave when connected in series and when connected in parallel.

Find at the terminals of the circuit in Fig. 6.75.

Find the equivalent inductance looking into the terminals of the circuit in Fig. 6.76.

Find in each of the circuits in Fig. 6.77.

Find in the circuit of Fig. 6.78.

Determine that may be used to represent the inductive network of Fig. 6.79 at the terminals.

The current waveform in Fig. 6.80 flows through a 3-H inductor. Sketch the voltage across the inductor over the interval 0 6 t 6 6 s.

(a) For two inductors in series as in Fig. 6.81(a), show that the voltage division principle is assuming that the initial conditions are zero. (b) For two inductors in parallel as in Fig. 6.81(b), show that the current-division principle is assuming that the initial conditions are zero.

In the circuit of Fig. 6.82, Determine and for v t 7 0. o i (t) o(t) io(0) 2 A.

Consider the circuit in Fig. 6.83. Find: (a) and if (b) (c) energy stored in the 20-mH inductor at t 1 s.

Consider the circuit in Fig. 6.84. Given that for and find: (a) (b) and i2 i (t). 1 i (t) 2(0), i1 v(t) 12e t 7 0 (0) 10 mA, 3t mV 6.

In the circuit of Fig. 6.85, sketch vo.

The switch in Fig. 6.86 has been in position A for a long time. At the switch moves from position A to B. The switch is a make-before-break type so that there is no interruption in the inductor current. Find: (a) for (b) just after the switch has been moved to position B, (c) long after the switch is in position v(t) B.

The inductors in Fig. 6.87 are initially charged and are connected to the black box at If and find: (a) the energy initially stored in each inductor, (b) the total energy delivered to the black box from to (c) and (d) i(t), t 0. i2 i (t), t 0, 1(t

The current i(t) through a 20-mH inductor is equal, in magnitude, to the voltage across it for all values of time. If find i(t).

An op amp integrator has R 50 k and C 0.04 mF. If the input voltage is vi 10 sin 50t mV, obtain the output voltage.

A 10-V dc voltage is applied to an integrator with R 50 k , C 100 mF t 0. 6. How long will it take for the op amp to saturate if the saturation voltages are 12 V and 12 V? Assume that the initial capacitor voltage was zero.

An op amp integrator with R 4 M and C 1 mF has the input waveform shown in Fig. 6.88. Plot the output waveform.

Using a single op amp, a capacitor, and resistors of 100 k or less, design a circuit to implement vo 50 t 0 vi(t) dt 1 Assume v t 0.

Show how you would use a single op amp to generate If the integrating capacitor is obtain the other component values.

At calculate due to the cascaded integrators in Fig. 6.89. Assume that the integrators are reset to 0 V at t 0.

Show that the circuit in Fig. 6.90 is a noninverting integrator.

The triangular waveform in Fig. 6.91(a) is applied to the input of the op amp differentiator in Fig. 6.91(b). Plot the output.

An op amp differentiator has and The input voltage is a ramp Find the output voltage.

A voltage waveform has the following characteristics: a positive slope of 20 V/s for 5 ms followed by a negative slope of 10 V/s for 10 ms. If the waveform is applied to a differentiator with C 10 mF, sketch the output voltage waveform.

The output of the op amp circuit in Fig. 6.92(a) is shown in Fig. 6.92(b). Let and Determine the input voltage waveform and sketch it.

Design an analog computer to simulate where and v 0 v (0) 0. 0(0) 2 d2 vo dt 2  2 dvo dt  vo

Design an analog computer circuit to solve the following ordinary differential equation. dy(t) dt 4y(t) f(t) where y(0) 1 V.

Figure 6.93 presents an analog computer designed to solve a differential equation. Assuming is known, set up the equation for f(t).

Design an analog computer to simulate the following equation: d2 v dt 2 5v 2f (t)

Design an op amp circuit such that where and are the input voltage and output voltage, respectively. vs vo vo 10vs  2 vsdt

Your laboratory has available a large number of capacitors rated at 300 V. To design a capacitor bank of rated at 600 V, how many capacitors are needed and how would you connect them? 10-mF 40 mF 10-m

An 8-mH inductor is used in a fusion power experiment. If the current through the inductor is find the power being delivered to the inductor and the energy stored in it at t 0.5 s. i(t) 5 sin2 pt

A square-wave generator produces the voltage waveform shown in Fig. 6.94(a). What kind of a circuit component is needed to convert the voltage waveform to the triangular current waveform shown in Fig. 6.94(b)? Calculate the value of the component, assuming that it is initially uncharged.

An electric motor can be modeled as a series combination of a resistor and 200-mH inductor. If a current flows through the series combination, find the voltage across the combination.