Questions and Answers of Schaum S Outline Of Electric Circuits

Given p = 3.14, find the period of v(t) = cos t + cos 2pt.
Let v1 = cos 200πt and v2 = cos 202πt. Show that v = v1 + v2 is periodic. Find its period, Vmax, and the times when v attains its maximum value.
Find the average and effective values of v1(t) in Fig. 6-24(a) and v2(t) in Fig. 6-24(b). 3 新 (a) 2 0 V₂(1) -3 (b)
The current through a series RL circuit with R = 5 Ω and L = 10 H is given in Fig. 6-10(a) where T = 1 s. Find the voltage across RL. ST (1) T (a)
Express v(t) = cos 5t sin(3t + 45°) as the sum of two cosine functions and find its period.
Convert v(t) = 3 cos 100t + 4 sin 100t to A sin(100t + θ).
Find Vavg and Veff of the half-rectified sine wave v(t) = { V/m = sin cot when sin ot > 0 when sin ot < 0 (15)
Find the average and effective value of v2(t) in Fig. 6-1(b) for V1 = 2, V2 = 1, T = 4T1. U2(1) -V₂ T₁ T
Find the average and effective values of the cosine wave v(t) = Vm cos (w t + θ).
Find the capacitor current in Problem 6.19 (Fig. 6-20) for all t.Data from Problem 6.19The narrow pulse is of Problem 6.18 enters a parallel combination of a 1-µF capacitor and a 1-MΩ resistor
Find Vavg and Veff of the periodic function v(t) where, for one period T, [V = 1%/%/ -Vo v(t): for 0 < t < T₁ for T₁ < t < 3T₁ Period T = 37₁ (18)
Find V3,avg and V3,eff in Fig. 6-1(c) for T = 100T1. Vo -Vo Vz(1) A A T₁ T n 1
The voltage u across a 1-H inductor consists of one cycle of a sinusoidal waveform as shown in Fig. 6-25(a).(a) Write the equation for v(t).(b) Find and plot the current through the inductor.(c) Find
Determine the relationship between R, R1, and R2 in Fig. 5-41 such that the circuit has a gain of v2/i1 = 106 V/A. R V₁ R₁ R₂ S load R₁
The network of Problem 4.18 has been redrawn in Fig. 4-35 for solution by the node voltage method. Obtain node voltages V1 and V2 and verify the currents obtained in Problem 4.18.Data from problem
Find v2 as a function of i1 in the circuit of Fig. 5-40(a). B A اله R www w Uz . RI
In Fig. 5-23 let R = 1 kΩ, C = 1 μF, and v1 = sin 2000t. Assuming v2(0) = 0, find v2 for t > 0. 1+ In B A + C D ㅎ.
A transducer generates a weak current i1 which feeds a load Rl and produces a voltage v2 across it. It is desired that v2 follow the signal with a constant gain of 108 regardless of the value of Rl.
In the differential equation 10−2 dv2/dt + v2 = vs, vs is the forcing function and v2 is the response. Design an op amp circuit to obtain v2 from vs.
In Fig. 5-24, R1 = Rf = 1 kΩ, C = 1 μF, and v1 = sin 2000t. Find v2. + VI R₁ www A B R₁ mi C 9+ £ 10-1₁ 2₂
Determine the resistor values which would produce a current-to-voltage conversion gain of v2/i1 = 108 V/A in the circuit of Fig. 5-42. i₁ B R R₁ R₂ ww load R₁
Design a circuit containing op amps to solve the following set of equations: y' + x = v₁ sl 2y + x² + 3x = -52
Find the output vo in the integrator-summer amplifier of Fig. 5-25, where the circuit has three inputs. v₁ (+ V3 R₁ ww R₂ R₂ A B C 2010-11
In the circuit of Fig. 5-38 change the 21-V source by a factor of k. Show that vC, i1, and v2 in Problem 5.13 are changed by the same factor, but Rin remains unchanged. 21 V 3 ΚΩ ww 8
The input to the circuit of Fig. 5-23 with RC = 1 is v1 = sin ω t. Write KCL at node B and solve for v2. +1 VI R B A + C D 3+ £ 10-41. 12
Find vo as a function of v1 and v2 in the circuit of Fig. 5-20. +1 +1 R₁ wi B A 2/₂ W R3 W UB VA R₂ 2°
Find v2 and vC in Problem 5.13 by replacing the circuit to the left of node C in Fig. 5-38 (including the 21-V battery and the 3-kΩ and 6-kΩ resistors) by its Thévenin equivalent.Data from Problem
Show that the output v2 in Fig. 5.54 is the same as the output of the integrator in Fig. 5-23.Data from Figure 5.54Data from figure 5-23 CV2 +1 매
Find v1 and v2 in Fig. 5-21. -06 V ΙΚΩ 3 ΚΩ ww +0.5 V τ 1 ΚΩ 2 ΚΩ 2 ΚΩ ww + 12
(a) Find the Thévenin equivalent of the circuit to the left of nodes A-B in Fig. 5-39(a) and then find v2 for Rl = 1 kΩ, 10 kΩ, and ∞.(b) Repeat for Fig. 5-39(c) and compare with part (a). 15
Find v2 in the leaky integrator of Fig. 5-24 with R1 = Rf = 1 kΩ, C = 1 μF, andData from figure 5-24 V₁: = [1V t> 0 โo t
Let Rs = 1 kΩ in the circuit of Fig. 5-22. Find v1,v2,vo,is,i1, and if as functions of vs for(a) Rf = ∞ and(b) Rf = 40 kΩ. RI i, i | + B τους U huma 5 ΚΩ A 9 ΚΩ Rf Ug 1.2 ΚΩ σκο
Design a circuit with x(t) as input to generate output y(t) which satisfies the following equation: (27) (1)x = (1)Á + (1), ÁZ + (1)„Á
Find i2 as a function of v1 in the circuit of Fig. 5-43. VI R₁ i₁ B A + 1 R₂ B R₂
Average power delivered by a 1 mV voltage source to a 1 Ω resistor is 1 μW. Apply the 1 mV voltage source to the input of an amplifier with a gain of 60 dB and then connect the output to the 1 Ω
Design an op amp circuit as an ideal voltage source v(t) satisfying the equation v′ + v = 0 for t > 0, with v(0) = 1 V.
A practical current source (is in parallel with internal resistance Rs) directly feeds a load Rl as in Fig. 5-44(a).(a) Find load current il.(b) Place an op amp between the source and the load as in
The input-output relationship in a circuit is(a)(b)Plot the magnitude of the output (in dB) and its phase (in degrees) as functions of f for 10 5. Use logarithmic scale for frequency axis. dv₂ dt =
In Example 5.18 let v1 = sin ω t. Find |v2| for ω = 0, 10, 100, 103, 104, and 105 rad/s.Data from Example 5.18In Fig. 5-24, R1 = Rf = 1 kΩ, C = 1 μF, and v1 = sin 2000t. Find v2.
The input-output relationship in a circuit isDetermine(a) The dc gain,(b) The 3-dB attenuation frequency, and(c) The frequency at which V2 = 1. du, dt ₂ + 10¹v₂ = 10° v₁ -10%
Find vo in the circuit of Fig. 5-45. 5 120 R www R₁ R V3 R₁ R₂ www 9+2 10411
Find the gain of the filter of Example 5.18 as a function of frequency and express it in dB. Specify(a) Its dc value,(b) The 3-dB attenuation frequency,(c) Its value at 10 kHz, and(d) Its
Repeat Problem 5.51 for a circuit with the input-output relationshipData from Problem 5.51The input-output relationship in a circuit isDetermine(a) The dc gain,(b) The 3-dB attenuation frequency,
Find vo in the circuit of Fig. 5-46. + R₁ W 22 B A R₂ ww Vo
In the inverting-amplifier circuit of Fig. 5-11, assume Ri = ∞, Ro = 0, and a real-valued gain A. Develop an expression for v2/v1 in terms of k ≡ R2/R1 and A. R₁ mi V₁ B 1 Va A U+ R₂ R₂ A
Find vo in the circuit of Fig. 5-47. R2 w In R₁ V3 R₁ 2 R2 충%
In the inverting configuration of Fig. 5-13 switch the inverting and noninverting inputs of the op amp so that the inverting input is connected to the ground and a positive feedback is provided to
In Fig. 5-48 choose resistors for a differential gain of 106 so that vo = 106 (v2 − v1). VjO U₂0 + B R₁ ww R₁ R₂ R₂ Vo
Develop an expression for v2/v1 in the amplifier circuit of Fig. 5-11 in terms of the circuit elements and k ≡ R2/R1. The gain A of the op amp is a real-valued number. V1 R₁ B 1 Va A
Find v/i in Fig. 5-57, assuming an ideal op-amp with saturation levels at ± Vs. Segment ABC Segment CF Segment FGH v = R₂i - V₁ i R₂ v = R₁ R₁₂ v = R₂i + V₂ low saturation linear
Resistors having high magnitude and accuracy are expensive. Show that in the circuit of Fig. 5-49 we can choose resistors of ordinary range so that vo = 106 (v2 − v1).
In the circuit of Fig. 5-57. switch the inverting and noninverting inputs of the op amp so that the external lead goes to the inverting input and a positive feedback is provided to the op amp through
At low frequencies the magnitude open-loop gain of a 741 op amp varies aswhere typically a0 = 200,000 and f0 = 5 Hz. Find (a) Its dc gain in dB,(b) The 3-dB attenuation frequency, (c) The frequency
Show that in the circuit of Fig. 5-50 i1 = i2, regardless of the circuits N1 and N2. N₁ + 5 U₁ 15. R ww B Ol A + S 2₂ N₂
In Fig. 5-30, let Vcc = 5 V, vo = 0, and v1 = sin ωt. Find v2. V10- Vo + I Q+Vcc V cc 02
A sensor converts a physical quantity (such as heat, pressure, vibration, etc.) to an electrical signal. It is modeled by a voltage source vs in series with an internal resistance r. The sensor feeds
Repeat Problem 5.58 for the circuit shown in Fig. 5-63(a) with R1 = 2R2. Assume saturation levels of ±15 V. Given v1(t) = 10(sin 20πt + sin 30πt) and v2(0) = l5 V, sketch the output voltage v2(t).
Let N1 be the voltage source v1 and N2 be the resistor R2 in the circuit of Fig. 5-50. Find the input resistance Rin = v1/i1. N₁ + 5 U₁ R ww B Ol A + S 2₂ N₂
The circuit of Fig. 5-31 is a parallel analog-to-digital converter. The +Vcc and −Vcc connections are omitted for simplicity. Let Vcc = 5 V, vo = 4 V, and vi = t (V) for 0 3, v2, and v1. Interpret
The op amp of Fig. 5-30 compares the input signal v1 with an independent reference level v0, forcing the op amp into high saturation (if v1 > v0) or low saturation (if v1 0). Let the reference
A voltage follower is constructed using an op amp with a finite open-loop gain A and Rin = ∞ (see Fig. 5-51). Find the gain G = v2/v1. Defining sensitivity s as the ratio of percentage change
Compute the current in the 23-Ω resistor of Fig. 4-11(a) by applying the superposition principle. With the 200-V source acting alone, the 20-A current source is replaced by an open circuit, Fig.
In simple rectilinear motion, a 10-kg mass is given a constant acceleration of 2.0 m/s2.(a) Find the acting force F. (b) If the body was at rest at t=0, x = 0, find the position, kinetic energy, and
The force applied to an object moving in the x direction varies according to F= 12/x2 (N).(a) Find the work done in the interval 1 m ≤ x ≤ 3 m.(b) What constant force acting over the same
Obtain the work and power associated with a force of 7.5 × 10−4 N acting over a distance of 2 meters in an elapsed time of 14 seconds.
A conductor has a constant current of 5 amperes. How many electrons pass a fixed point on the conductor in 1 minute?
Electrical energy is converted to heat at the rate of 7.56 kJ/min in a resistor which has 270 C/min passing through. What is the voltage difference across the resistor terminals? From P = VI,
Obtain the work and power required to move a 5.0-kg mass up a frictionless plane inclined at an angle of 30° with the horizontal for a distance of 2.0 m along the plane in a time of 3.5 s.
In an electric circuit, an energy of 9.25 μJ is required to transport 0.5 μC from point a to point b. What electric potential difference exists between the two points?
A certain circuit element has a current i = 2.5 sin ωt (mA), where ω is the angular frequency in rad/s, and a voltage difference v = 45 sinωt (V) between its terminals. Find the average power Pavg
Work equal to 136.0 joules is expended in moving 8.5 × 1018 electrons between two points in an electric circuit. What potential difference does this establish between the two points?
A resistor has a potential difference of 50.0 V across its terminals and 120.0 C of charge per minute passes a fixed point. Under these conditions at what rate is electric energy converted to heat?
The unit of energy commonly used by electric utility companies is the kilowatt-hour (kWh).(a) How many joules are in 1 kWh?(b) A color television set rated at 75 W is operated from 7:00p.m. to 11:30
A pulse of electricity measures 305 V, 0.15 A, and lasts 500 μs. What power and energy does this represent?
An AWG #12 copper wire, a size in common use in residential wiring, contains approximately 2.77 × 1023 free electrons per meter length, assuming one free conduction electron per atom. What
A unit of power used for electric motors is the horsepower (hp), equal to 746 watts. How much energy does a 5-hp motor deliver in 2 hours? Express the answer in MJ.
How many electrons pass a fixed point in a 100-watt light bulb in 1 hour if the applied constant voltage is 120 V?
For t ≥ 0, q = (4.0 × 10−4)(1 − e−250t) (C). Obtain the current at t = 3 ms.
A certain circuit element has the current and voltageFind the total energy transferred during t ≥ 0. i= 10e-5000r (A) v = 50(1-e-5000) (V)
A typical 12 V auto battery is rated according to ampere-hours. A 70-Ah battery, for example, at a discharge rate of 3.5 A has a life of 20 h. (a) Assuming the voltage remains constant, obtain the
The capacitance of a circuit element is defined as Q/V, where Q is the magnitude of charge stored in the element and V is the magnitude of the voltage difference across the element. The SI derived
A resistor has a voltage of V = 1.5 mV. Obtain the current if the power absorbed is(a) 27.75 nW and (b) 1.20 μW.
A resistance of 5.0 Ω has a current i = 5.0 × 103 t (A) in the interval 0 ≤ t ≤ 2 ms. Obtain the instantaneous and average powers.
In the interval 0 < t < (π /50)s a 30-mH inductance has a current i = 10.0 sin 50t (A). Obtain the voltage, power, and energy for the inductance.
The current in a 5-Ω resistor increases linearly from zero to 10 A in 2 ms. At t = 2+ ms the current is again zero, and it increases linearly to 10 A at t = 4 ms. This pattern repeats each 2 ms.
An inductance of 2.0 mH has a current i = 5.0(1 − e−5000t)(A). Find the corresponding voltage and the maximum stored energy.
Current i enters a generalized circuit element at the positive terminal and the voltage across the element is 3.91 V. If the power absorbed is −25.0 mW, obtain the current.
In the interval 0 < t < 5π ms, a 20-μF capacitance has a voltage u = 50.0 sin 200t (V). Obtain the charge, power, and energy. Plot wC assuming w = 0 at t = 0.
An inductance of 3.0 mH has a voltage that is described as follows: for 0 < t < 2 ms, V = 15.0 V and for 2 < t < 4 ms, V = −30.0 V. Obtain the corresponding current and sketch VL and i for the
The current and voltage characteristic of a semiconductor diode in the forward direction is measured and recorded in the following table: v (V) i (mA) 0.5 0.6 2 x 10 0.11 0.65 0.66 1.2 0.78 0.67 0.68
Determine the single circuit element for which the current and voltage in the interval 0 ≤ 103 t ≤ p are given by i = 2.0 sin 103 t (mA) and v = 5.0 cos 103 t (mV).
A capacitance of 60.0 μF has a voltage described as follows: 0 3 t (V). Sketch i, p, and w for the given interval and find Wmax. UL 15.0 -30.0 0 t, ms 10.0 -10.0 1, ms.
A 20.0-μF capacitance is linearly charged from 0 to 400 μC in 5.0 ms. Find the voltage function and Wmax.
A capacitance of 2.0 μF with an initial charge Q0 is switched into a series circuit consisting of a 10.0-Ω resistance. Find Q0 if the energy dissipated in the resistance is 3.6 mJ.
A series circuit with R = 2Ω, L = 2 mH, and C = 500 μF has a current which increases linearly from zero to 10 A in the interval 0 ≤ t ≤ 1 ms, remains at 10 A for 1 ms ≤ t ≤ 2 ms, and
A single circuit element has the current and voltage functions graphed in Fig. 2-15. Determine the element. i, A 10 V. 0 -10 VI 15 0 -30 2 2 4 6 6 8 8 1, ms t, ms
Given that a capacitance of C farads has a current i = (Vm/R)e-t/(Rc) (A), show that the maximum stored energy is 1/2CV2m .Assume the initial charge is zero.
The current after t = 0 in a single circuit element is as shown in Fig. 2-20. Find the voltage across the element at t = 6.5 μs, if the element is(a) A resistor with resistance of 10 kΩ,(b) An
Obtain the voltage v in the branch shown in Fig. 2-16 for (a) i2 = 1 A, (b) i2 = −2 A,(c) i2 = 0 A.Voltage v is the sum of the current-independent 10-V source and the current-dependent voltage
The 20.0-μF capacitor in the circuit shown in Fig. 2-21 has a voltage for t > 0, v = 100.0e−t/0.015 (V). Obtain the energy function that accompanies the discharge of the capacitor and compare

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