Questions and Answers of Schaum S Outline Of Electric Circuits

The input voltage in the circuits of 7-45 is a weighted sum of sinusoids with the highest frequency f0 Hz. Assuming that RC 0), find v2(t). R W D B 3 M R G 2₁ R₁ R B (b) R₁ ww V/₂
The switch in Fig. 7-34 has been in position 1 for a long time; it is moved to 2 at t = 0. Obtain the expression for i, for t > 0. 50 V 10 V 2 40 Ω 20 mH
Find the relationship between v2 and v1 in the circuit of Fig. 7-46. +1 R₁ www R B R₁ ww + 12 12
The switch in the circuit shown in Fig. 7-35 is moved from 1 to 2 at t = 0. Find vC and vR, for t > 0. 100 V 50 V DR UC 5000 1 μF
In the circuit of Fig. 7-47, find the differential equation relating v2 to v1. Compare with the result of Example 7.17.Data from Example 7.17Find the relationship between v2 and v1 in the circuit of
Obtain the energy functions for the circuit of Problem 7.22.Data from problem 7.22The switch in the circuit shown in Fig. 7-35 is moved from 1 to 2 at t = 0. Find vC and vR, for t > 0. 100 V 50
In the circuit of Fig. 7-48, find the relationship between v2 and v1. +1 HH C₁ R₁ www R₂ + C₂ 22
A series RC circuit, with R = 5 kΩ and C = 20 μF, has two voltage sources in series. They are Obtain the complete expression for the voltage across the capacitor and make a sketch, if t′ is
Show that the segment of the circuit enclosed by the dashed box in the circuit of Fig. 7-49 is equivalent to an inductor with value L = 1/(1 − k) H. 2 V T t = 0 oko ww 292 292 ww + SI V B ele 1 H kV
In the circuit of Fig. 7-49, let k = 0. Find v and i after the switch is closed at t = 0. 2 V t = 0 охо ww 292 292 ww + S B roo 1 H kV
The switch in the circuit of Fig. 7-49 is closed at t = 0. Find v at t > 0 for the following values of k:(a) 0.5,(b) 1,(c) 2. 2 V T t=0 oxo ww 292 292 ww IS + V B roo 1 H kV
Find i, the current drawn from the battery, in Problem 7.50.Data from problem 7.50The switch in the circuit of Fig. 7-49 is closed at t = 0. Find v at t > 0 for the following values of
A 90 μF capacitor having an initial voltage of v0 = 6 V is connected at t = 0 to the input terminal of the circuit of Fig. 5-59, reproduced below in Fig. 7-51(a). Assume R1 = R2 = R3 = 1 kΩ and an
By observing that the circuit of 7-51 (a) is an inverting Schmitt trigger (introduced in Problem 5.58), argue that the capacitor voltage and the op amp’s output are correctly shown in Fig.
A 4.0-Ω resistor has a current i = 2.5 sin ω t (A). Find the voltage, power, and energy over one cycle, given that ω = 500 rad/s.
A 25.0-Ω resistance has a voltage v = 150.0 sin 377t (V).Find the corresponding current i and power p.
An inductance of 4.0 mH has a voltage v = 2.0e-103t (V). Obtain the maximum stored energy. At t = 0, the current
The current and voltage characteristic of a tungsten filament light bulb are measured and recorded in the following table. Voltages are DC steady-state values, applied for a long enough time for the
Find the output resistance seen by the output terminal pair ab in the circuit of Fig. 4-6. 60 V 8 ΤΩ 12 Ω e Ι C d 6Ω ΖΩ 5 Ω b
Repeat Problem 5.3 by replacing the circuit to the left of node A (include Ri) by its Thévenin equivalent (see Fig. 5-33). Solve the problem by applying the results of Example 5.4.Data from Problem
A practical voltage source vs with an internal resistance Rs is connected to the input of a voltage amplifier with input resistance Ri as in Fig. 5-2. Find v2/vs. 2 R₂ VI R₁ ww kv₁ Ro N VZ
In Fig. 5-3, let vs = 20 V, Rs = 10 Ω, Ri = 990 Ω, k = 5, and Ro = 3 Ω. Find(a) The Thévenin equivalent of the circuit seen by Rl and (b) v2 and the power dissipated in Rl for Rl = 0.5, 1, 3, 5,
Find the Thévenin equivalent of the circuit to the left of nodes A-B in Fig. 5-52 with k = 10 for(a) R2 = ∞ and(b) R2 = 50 kΩ. 10 V 10 ΚΩ Vd R₂ 100 Ω kud A B R₁
In Fig. 5-3 a practical voltage source us with internal resistance Rs feeds a load Rl through an amplifier with input and output resistances Ri and RO, respectively. Find v2/vs. 25 R₂ VI
In the circuits of Figs. 5-4 and 5-5 let R1 = 1 kΩ and R2 = 5 kΩ. Find the gains G+ = v2/vs in Fig. 5-4 and G− = v2/vs in Fig. 5-5 for k = 1, 2, 4, 6, 8, 10, 100, 1000, and ∞. Compare the
Repeat Problem 5.31 for R2 = 50 kΩ and k = 100.Data from Problem 5.31Find the Thévenin equivalent of the circuit to the left of nodes A-B in Fig. 5-52 with k = 10 for(a) R2 = ∞ and(b) R2 = 50
Find v2/vs in Fig. 5-4 and express it as a function of the ratio b = R1/(R1 + R2). Us R 1 + Uण A B R 2 kv₁ 02
Let R1 = 1 kΩ, R2 = 5 kΩ, and Ri = 50 kΩ in the circuit of Fig. 5-33. Find v2/vs for k = 1, 10, 100, 1000, ∞ and compare the results with the values of G− in Table 5-4.Data from Table 5.4
Let again R1 = 1 kΩ and R2 = 5 kΩ in the circuit of Fig. 5-33.(a) Find v2/vs as a function of k and Ri.(b) Let Ri = 1 kΩ. Find v2/v1 for k = 1, 10, 100, 1000, ∞. Repeat for Ri = ∞.(c) Discuss
In Fig. 5-5, R1 = 1 kΩ and R2 = 5 kΩ. (a) Find v2/vs as a function of the open-loop gain k.(b) Compute v2/vs for k = 100 and 1000 and discuss the results. +1 ww R₁ A U1 183 B R₂ kv₁ V2
In the circuit of Fig. 5-13, Vcc = 10 V, R1 = 2 kΩ and v1 = 1 V. Find the maximum value of R2 before the op amp is saturated. 10₁ R₁ B R₂ ww 2/2
Let again R1 = 1 kΩ and R2 = 5 kΩ in the circuit of Fig. 5-33. Replace the circuit to the left of node A (including Ri) by its Thévenin equivalent. Then use (5) to derive (44).
In the op amp of Fig. 5-8, Vcc = 15 V, A = 105, and v− = 0. Find the upper limit on the magnitude of v+ for linear operation. VO uto- R₁ R₂ A (U+- u) + Vo 1
Let the summing circuit of Fig. 5-14 have two inputs with v1 = 1 and v2 = sin t (V). Let R1 = 3 kΩ, R2 = 5 kΩ, and Rf = 8 kΩ. Apply superposition to find vo. V10 U₂0- V30- V40- Un
Find the output voltage of an op amp with A = 105 and Vcc = 10 V for v− = 0 and v+ = sin t (V). Refer to Figs. 5-7 and 5-8.Data from Figure 5-7Data from Figure 5-8 3° +Vcc Vcc A Vcc A -Vcc slope =
In the op amp of Fig. 5-8, Vcc = 5 V, A = 105, v− = 0 and v+ = 100 sin 2πt (μV). Find and sketch the open-loop output vo. UO uto- M R₁ www Ro A (U+-u) + Vo
In Fig. 5-17 let R1 = 4 kΩ and R2 = 8 kΩ. Apply superposition to find vo in terms of the input voltages. +1 2₂ +1 R R B R₂ R₁ Vo 10
Repeat Example 5.6 for v− = 25 μV and v+ = 50 sin 2πt (μV).Data from Example 5.6In the op amp of Fig. 5-8, Vcc = 5 V, A = 105, v− = 0 and v+ = 100 sin 2πt (μV). Find and sketch the open-loop
Repeat Problem 5.6 for v+ = sin 2πt (V) and v− = 0.5 V.Data from Problem 5.6Find the output voltage of an op amp with A = 105 and Vcc = 10 V for v− = 0 and v+ = sin t (V). Refer to Figs. 5-7 and
Find the input resistance seen by vf in Fig. 5-19. Uf R₁ mi www R₁ B A UB VA R₂ + R₂ mi + 2° 1
In the circuit of Fig. 5-35 vs = sin 100t. Find v1 and v2. v, = sin 100r 20 Ω τ 30 Ω B A 100 Ω www R
In Fig. 5-11, R1 = 10 kΩ, R2 = 50 kΩ, Ri = 500 kΩ, Ro = 0, and A = 105. Find v2/v1. Assume the amplifier is not saturated. 2₁ R₁ www B Vd + A U+ R₂ R₂ A (v+- u) 22 ww R₁
Use superposition to find vo in Fig. 5-20 for R1 = 2, R2 = 7, R3 = 10, R4 = 5, all in kΩ. +1 R₁ ww R3 ) 2 B A UB VA RA + R₂ +( Vo Į
The op amp in Fig. 5-12 is ideal and not saturated. Find(a) v2/v1;(b) The input resistance v1/i1; and(c) i1, i2, p1 (the power delivered by v1), and p2 (the power dissipated in the resistors), given
Saturation levels for the op amps in Fig. 5-31 are +Vcc = 5 V and −Vcc = −5 V. The reference voltage is vo = 1 V. Find the sequence of outputs corresponding to values of vi from 0 to 1 V in steps
In the circuit of Fig. 5-20 find(a) v0 for R1 = 1, R2 = 3, R3 = 2, and R4 = 2, all in kΩ; (b) The input resistance R2 in seen by v2; (c) i1 as a function of v1 and v2 and show that v1 sees a
Find v2/v1 in the circuit shown in Fig. 5-16. + 2 ΚΩ www ww 10 ΚΩ B A 15 5 ΚΩ + 7 ΚΩ U2 Rz
In the circuit of Fig. 5-37 find vC (the voltage at node C), i1, Rin (the input resistance seen by the 9-V source), v2, and i2. =9V webm 6 Ω 30 ww B A + US 大 100 2
Using a single op amp, design an amplifier with a gain of v2/v1 = 3/4, input resistance of 8 kΩ, and zero output resistance.
Find v2 in Problem 5.11 by replacing the circuit to the left of nodes A-B in Fig. 5-37 by its Thévenin equivalent.Data from Problem 5.11In the circuit of Fig. 5-37 find vC (the voltage at node C),
Determine vo in Fig. 5-17 in terms of v1, v2, v3, and the circuit elements. V1 +1 U₂+ R V3 +1. R B R₁ Vo
Show that, given R1 = ∞ and R2 = 0, the noninverting op amp circuit of Fig. 5-15 and (12) is reduced to a voltage follower. 1 R₁ B A R2 m U2 I
Find vC, i1, v2, and Rin (the input resistance seen by the 21-V source) in Fig. 5-38. 21 V 3 ΚΩ ww 8 ΚΩ σΚΩ ww 3 ΚΩ B A❤ 5 ΚΩ + D U2
(a) Find is,v1,v2, and il in Fig. 5-18(a).(b) Compare these results with those obtained when source and load are connected directly as in Fig. 5-18(b). R₂ voltage source 11, R₂ voltage
In the circuit of Fig. 5-22 let Rs = 10 kΩ.(a) Find Rf such that is = 0. (b) Is Rf independent of Rs? Discuss. R₂ Ug 1+ Ο B 5 ΚΩ A if 9 ΚΩ www Rf U2 1.2 ΚΩ ww σκΩ Jo
In a microwave range measurement system the electromagnetic signal v1 = A sin 2πft, with f = 100 MHz, is transmitted and its echo v2(t) from the target is recorded. The range is computed from τ,
Find period, frequency, phase angle in degrees, and maximum, minimum, average, and effective values of v(t) = 2 + 6 cos (10πt + π/6).
Show that if periods T1 and T2 of two periodic functions v1(t) and v2(t) have a common multiple, the sum of the two functions, v(t) = v1(t) + v2(t), is periodic with a period equal to the smallest
Reduce v(t) = 2 cos (ω t + 30°) + 3 cos ω t to v(t) = A sin (ω t + θ).
Plot v(t) = 5 cos (πt/6 + 30°) versus t and πt/6.
Find V2,avg and V2,eff in the graph of Fig. 6-1(b) for V1 = V2 = 3, and T = 4 T1/3. V₁ v₂(1) -V₂ T₁ T +1
Show that the average of cos2 (ω t + θ) is 1/2.
Referring to Fig. 6-1(d), let T = 6 and let the areas under the positive and negative sections of v4(t) be +5 and −3, respectively. Find the average and effective values of v4(t). V4(1) 2T
Compute the average power dissipated from 0 to T in a resistor connected to a voltage v(t). Replace v(t) by a constant voltage Vdc. Find Vdc such that the average power during the period remains the
The current i(t) shown in Fig. 6-6 passes through a 1-µF capacitor. Find(a) vac, the voltage across the capacitor at t = 5k ms (k = 0, 1, 2, 3, …) and (b) The value of a constant current source
Write the expression for v(t) which decays exponentially from 7 at t = 0 to 3 at t = ∞ with a time constant of 200 ms.
Find the average and effective value of the half-rectified cosine wave v1(t) shown in Fig. 6-17(a). T V₁ (1) V. 0 T 74 72 T (a) 37 T 5T t
The switch in the circuit of Fig. 6-8(a) is moved to position 2 at t = t0. Express vAB using the step function. 1 1 = 0 = S ОА + UAB 10 OB
Write the expression for v(t) which grows exponentially with a time constant of 0.8 s from zero at t = −∞ to 9 at t = 0.
Find the average and effective value of the full-rectified cosine wave v2(t) = Vm|cos 2πt/T | shown in Fig. 6-17(b). U₂(1) Vm 0 14 HIN 37 4 T ST t
Express the current of Fig. 6-6 in terms of step functions. 2 i(1), mA 0 نما 5 8 10 4. ms
If the switch in Fig. 6-8(a) is moved to position 2 at t = 0 and then moved back to position 1 at t = 5 s, express vAB using the step function. + 1=0 А 1 S ОА + VAB OB
A 100-mH inductor in series with 20-Ω resistor [Fig. 6-18(a)] carries a current i as shown in Fig. 6-18(b). Find and plot the voltages across R, L, and RL. + URL 2002. Ω 100 mH + VR + UL
In Fig. 6-10(a) let T = 1 s and call the waveform s1(t). Express s1(t) and its first two derivatives ds1/dt and d2s1 dt2, using step and impulse functions. ST (1) T
Express v(t), graphed in Fig. 6-9, using the step function. 1 -1 U(1) E 12m t
A radar signal s(t), with amplitude Vm = 100 V, consists of repeated tone bursts. Each tone burst lasts Tb = 50 μs. The bursts are repeated every Ts = 10 ms. Find Seff and the average power in s(t).
The voltage across the terminals of a 100-nF capacitor grows linearly, from 0 to 10 V, taking the shape of the function sT(t) in Fig. 6-10(a). Find(a) The charge across the capacitor at t = T and(b)
Find an impulse voltage which creates a 1-A current jump at t = 0 when applied across a 10-mH inductor.
(a) Given v1 = cos t, v2 = cos (t + 30°) and v = v1 + v2, write v in the form of a single cosine function v = A cos (t + θ). (b) Find effective values of v1, v2, and v. Discuss why Velf >
Let dT (t − t0) denote a narrow pulse of width T and height 1/T, which starts at t = t0. Consider a function f (t) which is continuous between t0 and t0 + T as shown in Fig. 6-11(a). Find the limit
An appliance uses Veff = 120 V at 60 Hz and draws Ieff = 10 A with a phase lag of 60°. Express v, i, and p = vi as functions of time and show that power is periodic with a dc value. Find the
A narrow pulse is of 1-A amplitude and 1-μs duration enters a 1-μF capacitor at t = 0, as shown in Fig. 6-19. The capacitor is initially uncharged. Find the voltage across the capacitor.
The narrow pulse is of Problem 6.18 enters a parallel combination of a 1-µF capacitor and a 1-MΩ resistor (Fig. 6-20). Assume the pulse ends at t = 0 and that the capacitor is initially uncharged.
(a) Show that v1 =+ cos t cos √2t is not periodic.(b) Replace √2 by 1.4 and then show that v2 = cos t + cos 1.4t is periodic and find its period T2.(c) Replace √2 by 1.41 and find the period T3
A random signal s(t) with an rms value of 5 V has a dc value of 2 V. Find the rms value of s0(t) = s(t) − 2, that is, when the dc component is removed.
Find the maximum and minimum values of v = 1 + 2 sin(ω t + θ), given ω = 1000 rad/s and θ = 3 rad. Determine if the function v is periodic, and find its frequency f and period T. Specify the
Let v1 = 8 sin 100πt and v2 = 6 sin 99πt. Show that v = v1 + v2 is periodic. Find the period, and the maximum, average, and effective values of v.
Graph each of the following functions and specify the period and frequency.(a) v1 (t) = cos t(b) v2 (t) = sin t(c) v3(t) = 2 cos 2πt(d)(e) v₂(t) = 2 cos (nt/4-45°) = 2 cos (лt/4/4)= 2 cos [л(1
Plot the function v(t) which varies exponentially from 5 V at t = 0 to 12 V at t = ∞ with a time constant of 2 s. Write the equation for v(t).
Samples from a random signal x(t) are recorded every 1 ms and designated by x(n). Approximate the mean and rms values of x(t) from samples given in Table 6-2. n 0 x(n) 2 1 4 2 11 3 5 769 4 5 6 7
The current i = I0e−at cos ω t passes through a series RL circuit.(a) Find vRL, the voltage across this combination.(b) Compute vRL for I0 = 3 A, a = 2, ω = 40 rad/s, R = 5 Ω and L = 0.1 H.
The voltage v = V0e−|t|/τ, τ > 0, is connected to a capacitor. Find the current i in the capacitor. Sketch v and i for V0 = 10 V, C = 1 µF, and τ = 1 ms.
(a) Show that the rate of change with respect to time of an exponential function v = Aest is at any moment proportional to the value of the function at that moment.(b) Show that any linear
The voltage v = V0e−a|t| for a > 0 is connected across a parallel combination of a resistor and a capacitor as shown in Fig. 6-22(a). (a) Find currents iC, iR, and i = iC + iR.(b) Compute and
Repeat Problem 6.25 for V1 = 0, V2 = 4, and T = 2T1.Data from problem 6.25Find V2,avg and V2,eff in the graph of Fig. 6-1(b) for V1 = V2 = 3, and T = 4 T1/3. 22(1) -V2 T₁ T
Find the period of v(t) = cos 5t + 3 sin (3t + 45°).
Find V3,avg and V3,eff in the graph of Fig. 6-1(c) for V0 = 2 and T = 200T1. hin A - Vo (1) fa T W
The signal v (t) in Fig. 6-16 is sinusoidal. Find its period and frequency. Express it in the form v(t) = A + B cos (ω t + θ) and find its average and rms values.
The waveform in Fig. 6-23 is sinusoidal. Express it in the form v = A + B sin (ω t + θ) and find its mean and rms values. -10 -2 O -5 ult) 5 f 1, S 15 20
Is v(t) = cos t + cos 2πt periodic? Discuss.

Showing 700 - 800 of 1036