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physics
electricity and magnetism
Fundamentals Of Electric Circuits 3rd Edition Matthew Sadiku, Charles Alexander - Solutions
Assuming R = 2kΩ, design a parallel RLC circuit that has the characteristic equation s2 + 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 α = 1?
The switch in Fig. 8.77 moves from position A to position B at t = 0 (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 > 0
In the circuit of Fig. 8.78, calculate io (t) and vo(t) for t > 0
The step response of an RLC circuit is described byGiven that i(0) = 2 and di(0) / dt = 4 , solve for i(t)
A branch voltage in an RLC circuit is described byIf the initial conditions are v(0) = 0 = dv(0)/ dt , find v(t).
A series RLC circuit is described byFind the response when L = 0.5H, R = Ω, and C = 0.2 F. Let i(0) = 1, di(0) / dt = 0 .
Solve the following differential equations subject to the specified initial conditions (a) d2v / dt2 + 4v = 12, v(0) = 0, dv(0) / dt = 2 (b) d2i / dt2 + 5 di / dt + 4i = 8, i(0) = -1, di(0) / dt = 0 (c) d2v / dt2 + 2 dv / dt + v = 3, v(0) = 5, dv(0) / dt = 1 (d) d2i / dt2 = 2 di / dt = 5i = 10,
Refer to the circuit shown in Fig. 8.64. Calculate:(a) iL (0+), vc (0+), and vR(0+),(b) diL (0+) / dt, diC(0+) / dt, and diR(0+) / dt,(c) iL(ˆž), vc(ˆž), and vR(ˆž).
The step responses of a series RLC circuit are vC = 40 - 10e-2000t - 10e-4000t V, t > 0 iL(t) = 3e-2000t + 6e-4000t t > 0 (a) Find C. (b) Determine what type of damping is exhibited by the circuit.
Consider the circuit in Fig. 8.79. Find vL(0+) and vC(0+)
For the circuit in Fig. 8.80, find v(t) for t > 0.
Find v(t) for t > 0 in the circuit of Fig. 8.81.
Calculate i(t) for t > 0 in the circuit of Fig. 8.82.
Determine v(t) for t > 0 in the circuit of Fig. 8.83.
Obtain v(t) and i(t) for t > 0 in the circuit of Fig. 8.84.
For the network in Fig. 8.85, solve for i(t) for t > 0.
Refer to the circuit in Fig. 8.86. Calculate i(t) for t > 0
Determine v(t) for t > 0 in the circuit of Fig. 8.87.
In the ciRcuit of Fig. 8.65, find:(a) v(0+), and i(0+),(b) dv(0+) / dt, di (0+) / dt, and di(0+) / dt,(c) v(ˆž),and i(ˆž).
The switch in the circuit of Fig. 8.88 is moved from position a to b at t = 0. Determine i(t) for t > 0 .
* For the network in Fig. 8.89, find i(t) for t > 0.
* Given the network in Fig. 8.90, find v(t) for t > 0.
The switch in Fig. 8.91 is opened at t = 0 after the circuit has reached steady state. Choose R and C such that α = 8Np/s and (d = 30 rad/s.
A series RLC circuit has the following parameters: R =1 kΩ, L =1H, and C = 10 nF. What type of damping does this circuit exhibit?
In the circuit of Fig. 8.92, find v(t) and i(t) for t > 0 . Assume v(0) = 0V and i(0) = 1A.
Find i(t) for t > 0 in the circuit of Fig. 8.93.
Find the output voltage vo(t) in the circuit of Fig. 8.94.
Given the circuit in Fig. 8.95, find i(t) and v(t) for t > 0.
Determine i(t) for t > 0 in the circuit of Fig. 8.96.
Refer to the circuit in Fig. 8.66. Determine:(a) i(0+), and c(0+),(b) di(0+) / dt and dv(0+) / dt,(c) i(ˆž),and v (ˆž).
For the circuit in Fig. 8.97, find i(t) for t > 0.
Find v(t) for t > 0 in the circuit of Fig. 8.98.
The step response of a parallel RLC circuit is v = 10 + 20e-300t (cos 400t - 2 sin 400t) V, t > 0 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 t = 0. Find the differential equation describing i(t), t > 0.
The switch in Fig. 8.100 moves from position A to B at t = 0. Determine:(a) i(0+) and v(0+),(b) di(0+) / dt,(c) i(ˆž) and v(ˆž).
For the circuit in Fig. 8.101, find v(t) for t > 0 . Assume that v(0+) = 4 V and i(0+) = 2A.
In the circuit of Fig. 8.102, find i(t) for t > 0 .
If the switch in Fig. 8.103 has been closed for a long time before t = 0, but is opened at t = 0 determine:(a) The characteristic equation of the circuit,(b) ix and vR for t > 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 t = 0 Find:(a) v(0+), dv(0+)/ dt(b) v(t) for t > 0
The make before break switch in Fig. 8.105 has been in position 1 for t
In the circuit of Fig. 8.67, find:(a) vR (0+), and vL(0+),(b) dvR (0+) / dt and dvL (0+) / dt,(c) vR (ˆž),and vL (ˆž).
Obtain i1 and i2 for t > 0 in the circuit of Fig. 8. 106.
For the circuit in Prob. 8.5, find i and v for t > 0.
Find the response vR(t) for t > 0 in the circuit of Fig. 8.107. Let R = 3Ω, L = 2H, C = 1/18F.
For the op amp circuit in Fig. 8.108, find the differential equation for i(t).
For the op amp circuit in Fig. 8.109, derive the differential equation relating vo to vs.
Determine the differential equation for the op amp circuit in Fig. 8.110. If v1(0+) = 2 V and v2(0+) = O V find vo for t > 0. Let R = 100kΩ and C = 1μF.
Obtain the differential equations for vo (t) in the op amp circuit of Fig. 8.111.
* In the op amp circuit of Fig. 8.112, determine vo(t) for t > 0. Let vin = u(t) V, R1 = R2 = 10kΩ, C1 = C2 = 100μF.
For the step function vs = u(t), use PSpice to find the response v(t) for 0
Given the source-free circuit in Fig. 8.114, use PSpice to get i(y) for 0
A series RLC circuit has R =10kΩ, L = 0.1 mH, and C = 10μF. What type of damping is exhibited by the circuit?
For the circuit in Fig. 8.115, use PSpice to obtain v(t) for 0
Obtain v(t) for 0
The switch in Fig. 8.117 has been in position 1 for a long time. At t = 0, it is switched to position 2. Use PSpice to find i(t) for 0
Rework Prob. 8.25 using PSpice. Plot vo (t) for 0 In Problem 8.25
The dual is constructed as shown in Fig. 8.118(a). The dual is redrawn as shown in Fig. 8.118(b).
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 R = 3Ω, C = 1/ 30 F, and L = 60 mH.
A load is modeled as a 250-mH inductor in parallel with a 12- Ω 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 branch current is described byDetermine: (a) The characteristic equation,(b) The type of damping exhibited by the circuit, (c) i(t) given that i(0) 1 and di(0) / dt = 2 .
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 50-k Ω 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 200- Ω 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:C1 = volume of fluid in a drugC2 = volume of blood stream in a specified regionR1 = Resistance in the passage of the drug from the input to the blood streamR2
Figure 8.124 shows a typical tunnel-diode oscillator circuit. The diode is modeled as a nonlinear resistor with iD = f(vD) 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 v and iD.
The current in an RLC circuit is described byIf i(0) = 10 and di(0) / dt = 0 find i(t) for t > 0.
Given the sinusoidal voltage v(t) = 50 cos (30t + 10o) V, find: (a) The amplitude Vm, (b) The period T, (c) The frequency f, and (d) v(t) at t = 10 ms.
Given that z1 = 6 - j8, z2 = 10 ∠ -30o, and z3 = 8e − j120o, find: (a) z1 + z2 + z3 (b) z1z2 / z3
Find the phasors corresponding to the following signals: (a) v(t) = 21 cos(4t - 15o) V (b) i(t) = -8 sin(10t + 70o) mA (c) v(t) = 120 sin (10t - 50o) V (d) i(t) = -60 cos(30t + 10o) mA
Let X = 8∠40o and and Y = 10 ∠− 30o Evaluate the following quantities and express your results in polar form: (a) (X + Y)X* (b) (X -Y)* (c) (X + Y) / X
Evaluate the following complex numbers:(a)(b)(c)
Simplify the following expressions:(a)(b)(c)
Evaluate these determinants:(a)(b)(c)
Transform the following sinusoids to phasors: (a) -10 cos (4t + 75o) (b) 5 sin(20t - 10o) (c) 4 cos2t + 3 sin 2t
Two voltages v1 and v2 appear in series so that their sum is v = v1 + v2. If v1 = 10 cos(50t - π/3) V and v2 = 12cos(50t + 30o) V, find v.
Obtain the sinusoids corresponding to each of the following phasors: (a) V1 = 60 ∠ 15o V, ω = 1 (b) V2 = 6 + j8 V, ω = 40 (c) I1 = 2.8e − jπ3 A, ω = 377 (d) I2 = -0.5 - j1.2 A, ω = 103
Using phasors, find: (a) 3cos(20t + 10º) - 5 cos(20t- 30º) (b) 40 sin 50t + 30 cos(50t - 45º) (c) 20 sin 400t + 10 cos(400t + 60º) -5 sin(400t - 20º)
A current source in a linear circuit has is = 8 cos (500π t - 25o) A (a) What is the amplitude of the current? (b) What is the angular frequency? (c) Find the frequency of the current. (d) Calculate is at t = 2ms.
A linear network has a current input 4cos(ω t + 20º)A and a voltage output 10 cos(ωt +110º) V. Determine the associated impedance.
Simplify the following:(a) f(t) = 5 cos(2t + 15(º) - 4sin(2t -30º)(b) g(t) = 8 sint + 4 cos(t + 50º)(c)
An alternating voltage is given by v(t) = 20 cos(5t - 30 o ) V. Use phasors to findAssume that the value of the integral is zero at t = - ˆž.
Apply phasor analysis to evaluate the following. (a) v = 50 cos(ω t + 30o) + 30 cos(ω t + 90o)V (b) i = 15 cos(ω t + 45o) - 10 sin(ω t + 45o)A
Find v(t) in the following integrodifferential equations using the phasor approach: (a) v(t) + ∫ v dt = 10 cost (b) dv / dt + 5v(t) + 4 ∫ v dt = 20 sin (4t + 10o)
Using phasors, determine i(t) in the following equations:(a) 2i / dt + 3i(t) 4cos(2t 45o)(b) 10 ∫ i dt + di + 6i (t) = 5cos(5t +22o)
The loop equation for a series RLC circuit givesAssuming that the value of the integral at t = - ˆž is zero, find i(t) using the phasor method.
A parallel RLC circuit has the node equation dv / dt = 50v + 100 ∫ v dt = 110cos(377t - 10o) Determine v(t) using the phasor method. You may assume that the value of the integral at t = - ∞ is zero.
Determine the current that flows through an 8- Ω resistor connected to a voltage source vs = 110 cos 377t V.
What is the instantaneous voltage across a 2-μ F capacitor when the current through it is i =4 sin(106 t +25o) A?
Express the following functions in cosine form: (a) 4 sin (ω t - 30o) (b) -2 sin 6t (c) -10sin(ω t + 20o)
A voltage v(t) = 100 cos(60t + 20o) V is applied to a parallel combination of a 40-k Ω resistor and a 50-μ F capacitor. Find the steady-state currents through the resistor and the capacitor.
A series RLC circuit has R = 80 Ω, L = 240 mH, and C = 5 mF. If the input voltage is v(t) = 10 cos 2t find the currrent flowing through the circuit.
For the network in Fig. 9.40, find the load current IL.
A series RL circuit is connected to a 110-V ac source. If the voltage across the resistor is 85 V, find the voltage across the inductor.
What value of ω will cause the forced response v o in Fig. 9.41 to be zero?
Find current i in the circuit of Fig. 9.42, when vs (t) = 50 cos200t V.
In the circuit of Fig. 9.43, determine i. Let vs = 60 cos(200t - 10o)V.
Determine the admittance Y for the circuit in Fig. 9.44.
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