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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

In the circuit of Fig. 7.93,v(t) = 20e ˆ’103t V, t > 0i(t) = 4e-103t mA, t > 0(a) Find R, L, and Ï„.(b) Calculate the energy dissipated in the resistance for 0
Calculate the time constant of the circuit in Fig. 7.94.
Find the time constant for each of the circuits in Fig. 7.95.(a)(b)
Determine the time constant for each of the circuits in Fig. 7.96.(a)(b)
Consider the circuit of Fig. 7.97. Find v0 (t) if i(0) = 2 A and v(t) = 0.
For the circuit in Fig. 7.98, determine v0 (t) when i(0) = 1 A and v(t) = 0.
In the circuit of Fig. 7.99, find i(t) for t > 0 if i(0) = 2 A.
Find the time constant for the RC circuit in Fig. 7.82.
For the circuit in Fig. 7.100,v = 120e ˆ’50t VAndi = 30e ˆ’50t A, t > 0(a) Find L and R.(b) Determine the time constant.(c) Calculate the initial energy in the inductor.(d) What
In the circuit of Fig. 7.101, find the value of R for which the steady-state energy stored in the inductor will be 1 J.
Find i(t) and v(t) for t > 0 in the circuit of Fig. 7.102 if i(0) = 10 A.
Consider the circuit in Fig. 7.103. Given that v 0 (0) = 2 V, find v 0 and v x for t > 0.
Express the following signals in terms of singularity functions.(a)(b)(c)(d)
Sketch each of the following waveforms. (a) i(t) = u(t -2) + u(t + 2) (b) v(t) = r(t) - r(t - 3) + 4u(t - 5) - 8u(t - 8)
Express the signals in Fig. 7.104 in terms of singularity functions.(a)(b) (c) (d)
Sketch the waveform represented by i(t) = r(t) - r(t -1) - u(t - 2) - r(t - 2) + r(t -3) + u(t - 4)
(a) x(t) = 10e−t u(t-1) (b) y(t) = 10e−(t−1) u(t) (c) z(t) = cos 4t δ (t - 1)
Determine the time constant for the circuit in Fig. 7.83.
Evaluate the following integrals involving the impulse functions:(a)(b)
Evaluate the following integrals:(a)(b)
Evaluate the following integrals:(a)(b)(c)
The voltage across a 10-mH inductor is 20 δ (t -2) mV. Find the inductor current, assuming that the inductor is initially uncharged.
Evaluate the following derivatives: (a) d / dt [u(t - 1) u(t + 1)] (b) d /dt [r(t - 6) u(t - 2)] (c) d /dt [sin 4tu(t - 31)]
Find the solution to the following differential equations: (a) dv / dt + 2v = 0, v(0) = -1v (b) 2 di / dt + 3i = 0, i(0) = 2
Solve for v in the following differential equations, subject to the stated initial condition. (a) dv / dt + v = u(t), v(0) = 0 (b) 2 dv / dt - v =3u(t), v(0) = -6
A circuit is described by 4 dv / dt + v = 10 (a) What is the time constant of the circuit? (b) What is v(∞) the final value of v? (c) If v(0) = 2 find v(t) for t ≥ 0.
A circuit is described by di / dt + 3i = 2u(t) Find i(t) for t > 0 given that i(0) = 0.
Calculate the capacitor voltage for t 0 for each of the circuits in Fig. 7.106.(a)(b)
The switch in Fig. 7.84 moves instantaneously from A to B at t = 0. Find v for t > 0.
Find the capacitor voltage for t 0 for each of the circuits in Fig. 7.107.(a)(b)
For the circuit in Fig. 7.108, find v(t) for t > 0.
(a) If the switch in Fig. 7.109 has been open for a long time and is closed at t = 0, findvo (t).(b) Suppose that the switch has been closed for a long time and is opened at t = 0. Findvo (t).
Consider the circuit in Fig. 7.110. Find i(t) for t 0.
The switch in Fig. 7.111 has been in position a for a long time. At t = 0 it moves to position b. Calculate i(t) for all t > 0.
Find vo in the circuit of Fig. 7.112 when vs = 6u(t). Assume that vo (0) = 1 V.
For the circuit in Fig. 7.113, is(t) = 5u(t) Find v(t).
Determine v(t) for t > 0 in the circuit of Fig. 7.114 if v(0) = 0.
Find v(t) and i(t) in the circuit of Fig. 7.115.
If the waveform in Fig. 7.116(a) is applied to the circuit of Fig. 7.116(b), find v(t).Assume v(0) = 0.
For the circuit shown in Fig. 7.85, find i(t), t > 0.
* In the circuit of Fig. 7.117, find ix for t > 0. Let R1 = R2 = 1k Î©, R3 = 2k Î© , and C = 0.25 mF.
Rather than applying the short-cut technique used in Section 7.6, use KVL to obtain Eq. (7.60).
For the circuit in Fig. 7.118, find i(t) for t > 0.
Determine the inductor current i(t) for both t 0 for each of the circuits in Fig.7.119.(a)(b)
Obtain the inductor current for both t 0 in each of the circuits in Fig. 7.120.(a)(b)
Find v(t) for t 0 in the circuit of Fig. 7.121.
For the network shown in Fig. 7.122, find v(t) for t > 0.
* Find i1 (t) and i2 (t) for t > 0 in the circuit of Fig. 7.123.
Rework Prob. 7.17 if i(0) = 10 A and v(t) = 20u (t) V.
Determine the step response v0(t) to vs in the circuit of Fig. 7.124.
The switch in Fig. 7.86 has been closed for a long time, and it opens at t = 0. Find v(t) fort ‰¥ 0.
Find v(t) for t > 0 in the circuit of Fig. 7.125 if the initial current in the inductor is zero.
In the circuit of Fig. 7.126, is changes from 5 A to 10 A at t = 0 that is, is = 5u (-t) + 10u(t) Find v and i.
For the circuit in Fig. 7.127, calculate i(t) if i(0) = 0.
Obtain v(t) and i(t) in the circuit of Fig. 7.128.
Find v0 (t) for t > 0 in the circuit of Fig. 7.129
If the input pulse in Fig. 7.130(a) is applied to the circuit in Fig. 7.130(b), determine the response i(t).
For the op amp circuit of Fig. 7.131, find v0. Assume that vs changes abruptly from 0 to 1 V at t = 0.
If v(0) = 5 V, find v0 (t) for t > 0 in the op amp circuit of Fig. 7.132. Let R = 10k Î© and C = 1 Î¼ F.
Obtain v0 for t > 0 in the circuit of Fig. 7.133.
For the op amp circuit in Fig. 7.134, find v0 (t) for t > 0.
Assuming that the switch in Fig. 7.87 has been in position A for a long time and is moved to position B at t =0, find v0 (t) for t ‰¥ 0.
Determine v0 for t > 0 when vs = 20 mV in the op amp circuit of Fig. 7.135.
For the op amp circuit in Fig. 7.136, suppose v0 = 0 and vs = 3 V. Find v(t) for t > 0.
Find i 0 in the op amp circuit in Fig. 7.137. Assume that v(0) = -2 V, R = 10 k Î© , and C = 10 Î¼F.
For the op amp circuit in Fig. 7.138, let R1 = 10 k Î©, Rf = 20 k Î©, C = 20 Î¼ F, and v(0) = 1 V. Find v0.
Determine v0 (t) for t > 0 in the circuit of Fig. 7.139. Let is = 10u(t) Î¼ A and assume that the capacitor is initially uncharged.
In the circuit of Fig. 7.140, find v0 and i0, given that vs = 4u(t) V and v(0) = 1 V.
Repeat Prob. Using PSpice.In Problem 7.49If the waveform in Fig. 7.116(a) is applied to the circuit of Fig. 7.116(b), find v(t).Assume v(0) = 0.
The switch in Fig. 7.141 opens at t = 0. Use PSpice to determine v(t) for t > 0.
The switch in Fig. 7.142 moves from position a to b at t = 0. Use PSpice to find i(t) for t > 0.
In the circuit of Fig. 7.143, the switch has been in position a for a long time but moves instantaneously to position b at t = 0 Determine i0(t).
For the circuit in Fig. 7.88, ifv = 10e ˆ’4t V and i = 0.2e ˆ’ 4t A, t > 0(a) Find R and C.(b) Determine the time constant.(c) Calculate the initial energy in the capacitor.(d) -Obtain the
In the circuit of Fig. 7.144, assume that the switch has been in position a for a long time, find:(a) i1(0), i2 (0), and v0 (0)(b) iL(t)(c) i1(ˆž), i2 ( ˆž ), and v0
Repeat prob. 7.65 using PSpice.In Problem 7.65If the input pulse in Fig. 7.130(a) is applied to the circuit in Fig. 7.130(b), determine the response i(t).
v(∞) = 120, v(0) = 0, τ = RC = 34x106 x15x10−6 = 510s v(t) = v(∞) +[v(0) − v(∞)]e−t /τ ⎯⎯→ 85.6 = 120(1− e−t / 510)
The resistance of a 160-mH coil is 8 Ω. Find the time required for the current to build up to 60 percent of its final value when voltage is applied to the coil.
A simple relaxation oscillator circuit is shown in Fig. 7.145. The neon lamp fires when its voltage reaches 75 V and turns off when its voltage drops to 30 V. Its resistance is 120 Î© when
Figure 7.146 shows a circuit for setting the length of time voltage is applied to the electrodes of a welding machine. The time is taken as how long it takes the capacitor to charge from 0 to 8 V.
A 120-V dc generator energizes a motor whose coil has an inductance of 50 H and a resistance of 100 Î©. A field discharge resistor of 400 Î© is connected in parallel with the
The circuit in Fig. 7.148(a) can be designed as an approximate differentiator or an integrator, depending on whether the output is taken across the resistor or the capacitor, and also on the time
An RL circuit may be used as a differentiator if the output is taken across the inductor and τ
The switch in Fig. 7.89 opens at t = 0. Find v0 for t > 0
An attenuator probe employed with oscilloscopes was designed to reduce the magnitude of the input voltage vi by a factor of 10. As shown in Fig. 7.149, the oscilloscope has internal resistance Rs and
The circuit in Fig. 7.150 is used by a biology student to study "frog kick." She noticed that the frog kicked a little when the switch was closed but kicked violently for 5 s when the switch was
To move a spot of a cathode-ray tube across the screen requires a linear increase in the voltage across the deflection plates, as shown in Fig. 7.151. Given that the capacitance of the plates is 4
For the circuit in Fig. 8.62, find:(a) i(0+) and v(0+),(b) di(0+) / dt and dv(0+)dt,(c) i(ˆž) and (ˆž),
The differential equation that describes the voltage in an RLC network isGiven that v(0) = 0 , dv(0) / dt = 10 obtain v(t).
The natural response of an RLC circuit is described by the differential equationFor which the initial conditions are v(0) = 10 and dv(0) / dt = 0 Solve for v(t)
If R = 20Ω, L = 0.6H 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 t = 0 (please note that the switch must connect to point B before it breaks the connection at A, a make-before-break switch). Find v(t)
The responses of a series RLC circuit are vc (t) = 30 - 10e-20t + 30e-10t V iL (t) = 40-20t - 60-10t mA Where vc and iL are the capacitor voltage and inductor current, respectively. Determine the
Find i(t) for t > 0 in the circuit of Fig. 8.70.
In the circuit of Fig. 8.71, the switch instantaneously moves from position A to B at t = 0 Find v(t) for all t > 0
Find the voltage across the capacitor as a function of time for t > 0 for the circuit in Fig. 8.72. Assume steady-state conditions exist at t = 0-
Obtain v (t) for t > 0 in the circuit of Fig. 8.73.
In the ciRcuit of Fig. 8.63, determine:(a) iR (0+), iL (0+), and iC(0+),(b) diR (0+) / dt, diL(0+) / dt, and diC(0+) / dt,(c) iR(ˆž), iL(ˆž), and iC(ˆž).
The switch in the circuit of Fig. 8.74 has been closed for a long time but is opened att = 0 Determine i(t)for t > 0 .
* Calculate v(t) for t > 0 in the circuit of Fig. 8.75.

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