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**Unformatted text preview: **58 Chapter 3 Alternating Current Circuits I 3-6 QUESTIONS AND PROBLEMS 1. Complete the following summary table. Resistance Capacitance
general v-i di
relationship dt
dc relationship I = 0
resistance or R
reactance
impedance R + j0
v-i vector — j
relationship 19C 2. A sine wave signal (20 V PP) is connected to a 10 k0 A resistor. Calculate the current through the resistor in terms of
average, rms, and peak currents. What wattage rating should
the resistor have? 3. Determine the relationships among VP, me and VPP
for a square wave of amplitude i VP. 4. Determine the relationships among VP, VW, and VPP
for a triangular wave of amplitude : VP, for which the de— scription between 0 and ’lT/2 is v = 7% tot.
’IT 5. Compare the rms currents and power dissipations that
would occur if the waveforms of problems 2, 3 and 4 were
applied in turn to a 10 k0 resistor; in all cases, VPP= 20 V. 6. Calculate the magnitude and phase angle of the imped-
ance for the circuit of Figure A. lOkQ
150 Hz 0.2 uF FIGURE A Circuit for problems 6, 7, 8, 9 and 10. 7. At what frequency will the phase angle be 30° for the
circuit of Figure A? 8. Using the circuit values of Figure A, plot vow/vin
(where Vom is taken across the capacitor) versus the log of
frequency. Also plot the log of vent/vin versus the log of frequency. 9. Again using the circuit values of Figure A, make the
same plots as in problem 8, but taking vout across the
resistor. 10. With reference to the plots of problems 8 and 9, is
there a frequency at which vow/v,n is the same in both cases?
Explain. 11. Determine the resonance frequency for the series cir-
cuit of Figure B. HH—ar—o 2 ”F 1 k9
FIGURE B Circuit for problems 11 and 12. 12. Calculate the magnitude and phase angle of the
impedance of the circuit in Figure B when it is operated at
2500 Hz. 13. What value of L is necessary for resonance at 10,000
Hz for the circuit of Figure C when R = 570 .Q and C =
0.01 uF? 14. Given that L = 0.05 H in the circuit of Figure C,
and the values of R and C as in problem 13, calculate the phase angle and magnitude of the impedance of the circuit at
100 kHz. 15. For the R, L and C values in problem 14, what are the
Q values of the circuit of Figure C at 100 kHz, 1000 Hz, and
100 Hz? FIGURE C Circuit for problems 13, 14 and 15. 16. For the high-pass ﬁlter of Figure D, at what frequency
is v /vin : 0.95? out 17. At what frequencies will the circuit of Figure D act as
a differentiator? o—I 0'1“}: 10m FIGURE D Circuit for problems 16, 17, 18 and 19. 18. Interchanging R and C of Figure D produces a low-
pass ﬁlter. At what frequency will vent/Vin = 0.95? 19. At what frequencies will the RC circuit of problem 18
2‘; act as an integrator? 20. Design a low—pass ﬁlter that has vow/vin = 0.5 at
1 5 kHz. _ 21. For the circuit that you designed in problem 20, at
f what frequencies will vow/vin equal 0.01 and 0.99? : 22. Consider an RLC series circuit in which R = 1 k0, L
= 1 H and C = 0.1 uF. calculate the resonance frequency,
‘A the impedance at resonance and the current at resonance } when Vrms = 10 V. Also sketch XL, XC, d) and Z as functions 2 of frequency. : 23. Consider an RLC parallel circuit, as in Figure C, in
Q which the component values are R = 1 k0, C = 0.1 uF, 24. Derive the following gain expression for the circuit of
L Figure B: Y.» ____Rﬁ__
vs R2+R1 (1 +ooCR2) FIGURE E Circuit for problems 24 and 25. Under what frequency conditions will the circuit of
Figure E behave as a simple voltage divider? and L = l H. Sketch Z, In,” and (l) as functions of frequency. Chapter 3 Alternating Current Circuits I 59 26. Derive the following gain expression for the circuit of
Figure F: FIGURE F Circuit for problems 26, 27 and 28. 27. Under what conditions of R and C will the gain of the
circuit of Figure F be the same as that of a simple voltage divider?
28. Suggest a possible use for the circuit of Figure F. 29. Consider the circuit of Figure G, where R1 -= 20 0,
X1 = 37.7 (1, R2 = 10 Q, and X2 = —53.1 9. Compute
the current and the phase angle between the current and the
applied voltage. 30. Determine the values of L and C used in problem 29. FIGURE G Circuit for problems 29 and 30. ...

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