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Figure P420
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421 Find the rms value of the waveform of Figure
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P421
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i(t) (A) 10 10 sin2t
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417 The voltage across and the current through a
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Figure P421
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Figure P417
422 Find the rms voltage of the waveform of Figure
P422
v(t)
Section 2: Time-Dependent Waveforms 418 Find the rms value of x(t) if x(t) is a sinusoid that
is offset by a DC value: x(t) = 2 sin( t) + 25
Vm T
419 For the waveform of Figure P419:
i(t) (A) 10 10 sin(t)
Figure P422
423 Find the rms value of the waveform shown in
2 0 1 2 2 + 1 3 2 t
Figure P423
i(t) (A) 2
10 0 < 1 < 2 = + 1
T 2 T 4 T 4 T 2 3T 4 T t
Figure P419
a Find the rms current b If 1 is /2, what is the rms current of this waveform
Figure P423
420 Find the rms value of the waveform of Figure
P420
424 Determine the rms (or effective) value of:
v(t) = VDC + vAC = 50 + 707 cos (377t) V
Part I
Circuits
Section 3: Phasor Analysis 425 If the current through and the voltage across a
component in an electrical circuit are:
i(t) = 17 cos[ t 12 ] mA v(t) = 35 cos[ t + 1309] V
429 If the current through and the voltage across an
electrical component are: i(t) = Io cos( t + ) 4 where: Io = 3 mA Vo = 700 mV = 6283 rad/s v(t) = Vo cos t
where = 6283 rad/s, determine: a Whether the component is a resistor, capacitor, or inductor b The value of the component in ohms, farads, or henrys
426 Describe the sinusoidal waveform shown in Figure
P426 using time-dependent and phasor notation
v (vt) (V) 170
a Is the component inductive or capacitive b Plot the instantaneous power p(t) as a function of t over the range 0 < t < 2 c Determine the average power dissipated as heat in the component d Repeat parts (b) and (c) if the phase angle of the current is changed to zero degrees
430 Determine the equivalent impedance in the circuit
shown in Figure P430: vs (t) = 7 cos 3,000t +
vt (rad) 2
2 170
R1 = 23 k L = 190 mH
R2 = 11 k C = 55 nF
Figure P426
427 Describe the sinusoidal waveform shown in Figure
P427 using time-dependent and phasor notation
i (vt) (mA) 8 2 2 8 8 ma vt (rad)
+ + v _ S _
R1 L
R2 C
Figure P430
431 Determine the equivalent impedance in the circuit
shown in Figure P430:
vs (t) = 636 cos 3,000t + 12 V R1 = 33 k R2 = 22 k L = 190 H C = 68 nF
Figure P427
432 In the circuit of Figure P432,
is (t) = Io cos t + 6 Io = 13 mA = 1,000 rad/s C = 05 F
428 Describe the sinusoidal waveform shown in Figure
P428 using time-dependent and phasor notation
i (vt) (mA) 8 2 2 8 8 ma vt (rad)
Figure P432
Figure P428
a State, using phasor notation, the source current b Determine the impedance of the capacitor
4
AC Network Analysis
c Using phasor notation only and showing all work, determine the voltage across the capacitor, including its polarity
437 The coil resistor in series with L models the
internal losses of an inductor in the circuit of Figure P437 Determine the current supplied by the source if: vs (t) = Vo cos( t + 0) Vo = 10 V = 6 Mrad/s Rs = 50 Rc = 40 L = 20 H C = 125 nF
433 Determine i3 (t) in the circuit shown in Figure
P433, if: i1 (t) = 1414 cos( t + 2356) mA i2 (t) = 50 sin( t 0927) mA = 377 rad/s
Z1 i1 + + V _ S _ i2 Z2 i3 Z3
Rs + + v _ S _ C
Rc L
Figure P437
438 Using phasor techniques, solve for the current in
Figure P433
the circuit shown in Figure P438
4 2H i
434 Determine the current through Z3 in the circuit of
Figure P434 Vs1 Z1 Z2 Z3 = vs2 = 170 cos(377t) V = 59 0122 = 23 0 = 17 0192
+ V _ S _ + + V _ S _
vs(t) = 12 cos 3t V + _
1/6 F
Figure P438
439 Using phasor techniques, solve for the voltage, v,
in the circuit shown in Figure P439
Z1 Z3 Z2
is(t) = 10 cos 2t A 2 2H 1/2 F v(t)
Figure P434
Figure P439
435 Determine the frequency so that the current Ii and
the voltage Vo in the circuit of of Figure P435 are in phase Zs = 13,000 + j 3 R = 120 L = 19 mH C = 220 pF
440 Solve for I1 in the circuit shown in Figure P440
I1 I = 10
I2 j5
Figure P440
I1 Zs C
+ V _ i
+ Vo
441 Solve for V2 in the circuit shown in Figure P441
Assume = 2
2 + V1 V = 25 0 V + _ 3 5H + V2
Figure P435
436 In the circuit of Figure P435, determine the
frequency r at which Ii and Vo are in phase
Figure P441
Part I
Circuits
442 Find the current through the resistor in the circuit
shown in Figure P442
36 cos (3t /3) V + _ iR(t) iS(t) 100 F 100
2H 1/18 F v
Figure P446
447 Using phasor techniques, solve for i in the circuit
iS(t) = 1 cos (200 t)
shown in Figure P447
05 H 5
Figure P442
443 Find vout (t) for the circuit shown in Figure P443
10 6 cos 2t A
1H 1/2 F i
XL = 1 k vout XC = 10 k
Figure P447
448 Determine the Th venin equivalent circuit as seen e
Figure P443
444 For the circuit shown in Figure P444, nd the
impedance Z, given = 4 rad/s
1/4 H
by the load shown in Figure P448 if a vS (t) = 10 cos(1,000t) b vS (t) = 10 cos(1,000,000t)
L RS a C b + RL vout Source Filter RS = RL = 500 L = 10 mH C = 01 F Load
1/8 F
vS (t)
+ ~
Figure P444
445 Find the admittance, Y , for the circuit shown in
Figure P445, when = 5 rad/s
Figure P448
449 Find the Th venin equivalent of the circuit shown e
in Figure P449 as seen by the load resistor
1/10 F
4/5 H + ~
1,000
vin (t) = 12 cos 10t
100 F
vout (t)
Figure P445 Figure P449
Section 4: AC Circuit Analysis 450 Solve for i(t) in the circuit of Figure P450, using 446 Using phasor techniques, solve for v in the circuit
shown in Figure P446 phasor techniques, if vS (t) = 2 cos(2t), R1 = 4 R2 = 4 , L = 2 H, and C = 1 F 4 ,
4
AC Network Analysis
C i(t)
+ vS (t) ~
Figure P450
b If C3 = 47 F, L3 = 0098 H, R1 = 100 , R2 = 1 , vS (t) = 24 sin(2,000t), and vab = 0, what is the reactance of the unknown circuit element Is it a capacitor or an inductor What is its value c What frequency should be avoided by the source in this circuit, and why
451 Using mesh current analysis, determine the
currents i1 (t) and i2 (t) in the circuit shown in Figure P451
R1 = 100 L = 05 H
454 Compute the Th venin impedance seen by resistor e
R2 in Problem 450
455 Compute the Th venin voltage seen by the e
inductance, L, in Problem 452
456 Find the Th venin equivalent circuit as seen from e
terminals a-b for the circuit shown in Figure 456
R2 = 75 j2 a j8 8 b
vS (t) =15 cos 1,500t + ~ i1(t)
C = 1 F i2(t)
Figure P451
5 30 V _
452 Using node voltage methods, determine the
voltages v1 (t) and v2 (t) in the circuit shown in Figure P452
Figure P456
v1(t) C v2(t)
457 Compute the Th venin voltage seen by resistor R2 e
in Problem 450
iS (t) = 40 cos 100t A
458 Find the Norton equivalent circuit seen by resistor
R2 in Problem 450
R1 = 10 R2 = 40 C = 500 F L = 02 H
459 Write the two loop equations required to solve for
the loop currents in the circuit of Figure P459 in: a Integral-differential form b Phasor form
Figure P452
453 The circuit shown in Figure P453 is a Wheatstone
bridge that will allow you to determine the reactance of an inductor or a capacitor The circuit is adjusted by changing R1 and R2 until vab is zero
C3 L3 vS (t)
+ ~
Rs + v _s I1
C I2 R1
Figure P459
R1 b
460 Write the node equations required to solve for all
voltages and currents in the circuit of Figure P459 Assume all impedances and the two source voltages are known
461 In the circuit shown in Figure P461:
vs1 = 450 cos t V vs2 = 450 cos t V A solution of the circuit with the ground at node e as shown gives:
Figure P453
a Assuming that the circuit is balanced, that is, that vab = 0, determine X4 in terms of the circuit elements
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