Page 384 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 29] ALTERNATING-CURRENT CIRCUITS 369

29.7. Find the reactance of a 5-µF capacitor at 10 Hz and at 10 kHz.

29.8. A capacitor has a reactance of 200 at 1000 Hz. What is its capacitance?

29.9. A5-µF capacitor is connected to a 6-kHz alternating emf, and a current of 2 A flows. Find the effective magnitude
of the emf.

29.10. A5-µF capacitor draws 1 A when it is connected to a 60-V ac source. What is the frequency of the source?

29.11. A 25-µF capacitor is connected in series with a 50- resistor, and a 12-V, 60-Hz potential difference is applied. Find
the current in the circuit and the power dissipated in it.

29.12. A capacitor is connected in series with an 8- resistor, and the combination is placed across a 24-V, 1000-Hz power
source. A current of 2 A flows. Find (a) the capacitance of the capacitor, (b) the phase angle, and (c) the power
dissipated by the circuit.

29.13. A 0.1-H, 30- inductor is connected to a 50-V, 100-Hz power source. Find the current in the inductor and the power
dissipated in it.

29.14. The current in a resistor is 1 A when it is connected to a 50-V, 100-Hz power source. (a) How much inductive
reactance is required to reduce the current to 0.5 A? What value of L will accomplish this? (b) How much capacitive
reactance is required to reduce the current to 0.5 A? What value of C will accomplish this? (c) What will the current
be if the above inductance and capacitance are both placed in series with the resistor?

29.15. A pure resistor, a pure capacitor, and a pure inductor are connected in series across an ac power source. An ac
voltmeter placed across each of these circuit elements in turn reads 10, 20, and 30 V. What is the potential difference
of the source?

29.16. Aninductivecircuitwithapowerfactorof80percentconsumes750Wofpower.Whatminimumratinginvoltamperes
must its power source have?

29.17. An inductive load dissipates 75 W of power when it draws 1.0 A from a 120-V, 60-Hz power line. (a) What is
the power factor? (b) What capacitance should be connected in series in the circuit to increase the power factor to
100 percent? (c) What would the current then be? (d) How much power would the circuit then dissipate?

29.18. A circuit that consists of a capacitor in series with a 50- resistor draws 4 A from a 250-V, 200-Hz power source.
(a) How much power is dissipated? (b) What is the power factor? (c) What inductance should be connected in series
in the circuit to increase the power factor to 100 percent? (d) What would the current then be? (e) How much power
would the circuit then dissipate?

29.19. In a series circuit R = 100 , X L = 120 , and X C = 60 when it is connected to an 80-V ac power source.
Find (a) the current in the circuit, (b) the phase angle, and (c) the current if the frequency of the power source were
changed to the resonance frequency of the circuit.

29.20. A 10-µF capacitor, a 10-mH inductor, and a 10- resistor are connected in series with a 45-V, 400-Hz power source.
Find (a) the impedance of the circuit, (b) the current in it, (c) the power it dissipates, and (d) the minimum rating in
voltamperes of the power source.

29.21. (a) Find the resonance frequency f 0 of the circuit of Prob. 29.20. (b) What current will flow in the circuit if it is
connected to a 45-V power source whose frequency is f 0 ?(c) How much power will be dissipated by the circuit?
(d) What must be the minimum rating of the power source in voltamperes?

29.22. A 60-µF capacitor, a 0.3-H inductor, and a 50- resistor are connected in series with a 120-V, 60-Hz power source.
Find (a) the impedance of the circuit, (b) the current in it, (c) the power it dissipates, and (d) the minimum rating in
voltamperes of the power source.