The switch in Fig. 8.105 has been in position 1 for At it

For the circuit in Fig. 8.62, find: (a) and (b) and (c) and i() v(). dv(0 di(0 )dt,

Using Fig. 8.63, design a problem to help other students better understand finding initial and final values.

Refer to the circuit shown in Fig. 8.64. Calculate: (a) and (b) and (c) and iL(), vC(), vR(). dvR(0 diL(0 )dt, )

In the circuit of Fig. 8.65, find: (a) and (b) and (c) and v() i(). di(

Refer to the circuit in Fig. 8.66. Determine: (a) and (b) and (c) and i() v().

In the circuit of Fig. 8.67, find: (a) and (b) and (c) and vR() vL().

A series RLC circuit has and What type of damping is exhibited by the circuit?

Design a problem to help other students better understand source-free RLC circuits.

The current in an RLC circuit is described by d2 i dt 2 10 di dt 25i 0 C If i(0) 10 A and di(0)dt 0, find i(t) t 7 0.

The differential equation that describes the voltage in an RLC network is d2 v dt 2 5 dv dt 4v 0 for which the initial conditions are v(0) 10 V and dv(0)dt 0. Solve for v(t).

The natural response of an RLC circuit is described by the differential equation d2 v dt 2 2 dv dt v 0 for which the initial conditions are v(0) 10 V and dv(0)dt 0. v(t).

If what value of C will make an RLC series circuit: (a) overdamped, (b) critically damped, (c) underdamped?

For the circuit in Fig. 8.68, calculate the value of R needed to have a critically damped response.

The switch in Fig. 8.69 moves from position A to position B at (please note that the switch must connect to point B before it breaks the connection at A, a make-before-break switch). Let v(0) 0, find v(t) for t 7 0.

The responses of a series RLC circuit i(t) t 7 0 vC iL iL(t) 40e 20t 60e 10t mA vC(t) 30 10e 20t 30e 10t V F are where and are the capacitor voltage and inductor current, respectively. Determine the values of R, L, and C.

Find for in the circuit of Fig. 8.70.

In the circuit of Fig. 8.71, the switch instantaneously moves from position A to B at Find for all t 0.

Find the voltage across the capacitor as a function of time for for the circuit in Fig. 8.72. Assume steady-state conditions exist at t 0.

Obtain for in the circuit of Fig. 8.73.

The switch in the circuit of Fig. 8.74 has been closed for a long time but is opened at Determine for t 7 0.

Calculate for in the circuit of Fig. 8.75.

Assuming design a parallel RLC circuit that has the characteristic equation 2 100s 106 0.

For the network in Fig. 8.76, what value of C is needed to make the response underdamped with unity damping factor ( )?

The switch in Fig. 8.77 moves from position A to position B at (please note that the switch must connect to point B before it breaks the connection at A, a make-before-break switch). Determine i(t) for t 7 0.

Using Fig. 8.78, design a problem to help other students better understand source-free RLC circuits.

The step response of an RLC circuit is given by d2 i dt 2 2 di dt 5i 10 F Given that i(0) 2 di(0)dt 4, I and solve for i(t).

A branch voltage in an RLC circuit is described by d2 v dt 2 4 dv dt 8v 24 i(0) 2 di(0)dt 4, i(t). d2 If the initial conditions are v(0) 0 dv(0)dt, P find v(t).

A series RLC circuit is described by L d2 i dt 2 R di dt i C 10 v Find the response when L 0.5 H, R 4 , and C 0.2 F. Let i(0) 1, di(0)dt 0. L

Solve the following differential equations subject to the specified initial conditions (a) (b) (c) (d)

The step responses of a series RLC circuit are vC 40 10e 2000t 10e 4000t V, t 7 0 iL(t) 3e 2000t 6e 4000t mA, t 7 0 (a) Find C. (b) Determine what type of damping is exhibited by the circuit.

Consider the circuit in Fig. 8.79. Find and vC(0).

For the circuit in Fig. 8.80, find for v(t) t 7 0

Find for in the circuit of Fig. 8.81.

Calculate for in the circuit of Fig. 8.82.

Using Fig. 8.83, design a problem to help other students better understand the step response of series RLC circuits.

Obtain and for in the circuit of Fig. 8.84.

For the network in Fig. 8.85, solve for for i(t) t 7 0.

Refer to the circuit in Fig. 8.86. Calculate for t 7 0

Determine for in the circuit of Fig. 8.87.

The switch in the circuit of Fig. 8.88 is moved from position a to b at Determine for t 0. i(t) t 7 0.

For the network in Fig. 8.89, find for i(t) t 7 0.

Given the network in Fig. 8.90, find for v(t) t 7 0

The switch in Fig. 8.91 is opened at after the circuit has reached steady state. Choose R and C such that and a 8 Np/s d 30 rad/s. t

A series RLC circuit has the following parameters: and What type of damping does this circuit exhibit?

In the circuit of Fig. 8.92, find and

Using Fig. 8.93, design a problem to help other students better understand the step response of a parallel RLC circuit.

Find the output voltage in the circuit of Fig. 8.94.

Given the circuit in Fig. 8.95, find and for t 7 0.

Determine for in the circuit of Fig. 8.96.

For the circuit in Fig. 8.97, find for i(t) t 7 0.

Find for in the circuit of Fig. 8.98.

The step response of a parallel RLC circuit is when the inductor is 50 mH. Find R and C.

After being open for a day, the switch in the circuit of Fig. 8.99 is closed at Find the differential equation describing i(t), t 7 0.

Using Fig. 8.100, design a problem to help other students better understand general second-order circuits.

For the circuit in Fig. 8.101, find for Assume that and i(0 v(0 ) 2 A. )

In the circuit of Fig. 8.102, find for i(t) t 7 0.

If the switch in Fig. 8.103 has been closed for a long time before but is opened at determine: (a) the characteristic equation of the circuit, (b) and for i vR t 7 0.

In the circuit of Fig. 8.104, the switch has been in position 1 for a long time but moved to position 2 at Find: (a) (b) for v(t) t 0. v(0), dv(0)dt, t

The switch in Fig. 8.105 has been in position 1 for At it is moved from position 1 to the top of the capacitor at . Please note that the switch is a make before break switch, it stays in contact with position 1 until it makes contact with the top of the capacitor and then breaks the contact at position 1. Determine v(t).

Obtain and for in the circuit of Fig. 8.106.

For the circuit in Prob. 8.5, find i and v t 7 0

Find the response for in the circuit of Fig. 8.107. Let R 3 , L 2 H, and C 118 F. vR

For the op amp circuit in Fig. 8.108, find the differential equation for i(t).

Using Fig. 8.109, design a problem to help other students better understand second-order op amp circuits.

Determine the differential equation for the op amp circuit in Fig. 8.110. If and find for Let and C 1 mF.

Obtain the differential equations for in the op amp circuit of Fig. 8.111.

In the op amp circuit of Fig. 8.112, determine for Let C1 C2 100 mF.

For the step function use PSpice or MultiSim to find the response for in the circuit of Fig. 8.113.

Given the source-free circuit in Fig. 8.114, use PSpice or MultiSim to get for Take and v(0) 30 V i(0) 2 A. i(t) 0 6 t 6 20 s

For the circuit in Fig. 8.115, use PSpice or MultiSim to obtain for Assume that the capacitor voltage and inductor current at are both zero.

Obtain for in the circuit of Fig. 8.116 using PSpice or MultiSim.

The switch in Fig. 8.117 has been in position 1 for a long time. At it is switched to position 2. Use PSpice or MultiSim to find for 0 i(t) 6 t 6 0.2 s.

Design a problem, to be solved using PSpice or MultiSim, to help other students better understand source-free RLC circuits.

Draw the dual of the circuit shown in Fig. 8.118.

Obtain the dual of the circuit in Fig. 8.119.

Find the dual of the circuit in Fig. 8.120.

Draw the dual of the circuit in Fig. 8.121.

An automobile airbag igniter is modeled by the circuit in Fig. 8.122. Determine the time it takes the voltage across the igniter to reach its first peak after switching from A to B. Let and L 60 mH.

A load is modeled as a 250-mH inductor in parallel with a resistor. A capacitor is needed to be connected to the load so that the network is critically damped at 60 Hz. Calculate the size of the capacitor.

A mechanical system is modeled by a series RLC circuit. It is desired to produce an overdamped response with time constants 0.1 ms and 0.5 ms. If a series resistor is used, find the values of L and C.

An oscillogram can be adequately modeled by a second-order system in the form of a parallel RLC circuit. It is desired to give an underdamped voltage across a resistor. If the damping frequency is 4 kHz and the time constant of the envelope is 0.25 s, find the necessary values of L and C

The circuit in Fig. 8.123 is the electrical analog of body functions used in medical schools to study convulsions. The analog is as follows: Find for given that R and v0 60u(t) V. 5 mF, 1 5 M, R2 2.5 M, v(t) t 7 0 C1 0.5 mF, C2 v(t) Percentage of the drug in the blood stream v0 Initial concentration of the drug dosage such as kidney, etc. R2 Resistance of the excretion mechanism, the input to the blood stream R1 Resistance in the passage of the drug from C2 Volume of blood stream in a specified region C1 Volume of fluid in a drug 200- 50

Figure 8.124 shows a typical tunnel-diode oscillator circuit. The diode is modeled as a nonlinear resistor with i.e., the diode current is a nonlinear function of the voltage across the diode. Derive the differential equation for the circuit in terms of and v iD.