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CHAPTER 19: SERIES A.C. CIRCUITS
1.
A capacitor of capacitance 100 μF is connected across a 220-V, 60-Hz, supply.
What is (a) the capacitive reactancee of the capacitor, and (b) the resulting current?
[Answer: (a) 26.5 Ω; (b) 8.3 A]
2.
A voltage of 100 V, at a frequency of 50 Hz, is applied to a 0.2-H coil of
negligible resistance. What will be (a) the resulting current, and what will be the effect on
the current of (b) doubling the frequency, and (c) halving the frequency? [Answer: (a)
1.592 A; (b) the current will halve; (c) the current will double]
3.
A reactor, of negligible resistance, takes a current of 3.2 A when connected to a
200-V, 50-Hz, supply. What is (a) the value of its inductance, and (b) the value of current
if the frequency is reduced to 40 Hz. Answer: (a) [0.199 H; (b) 4 A.
4.
A circuit comprises a 250-Ω resistor in series with a 455 pF capacitor. What
frequency will result in a phase angle of 45°? [Answer: 1.4 MHz]
5.
Calculate the current drawn by a series resistive-inductive circuit of resistance
5 Ω and inductance 0.02 H, when supplied from a 200-V, 50-Hz, supply. What is the
value of the circuit’s phase angle, and is it leading or lagging? [Answer: 24.91 A; 51.5°
lagging]
6.
An inductor has a resistance of 4 Ω, and draws a current of 8 A from a 100-V, 50Hz, supply. Calculate the values of the inductor’s (a) inductive reactance, (b) inductance,
(c) impedance, and (d) phase angle. [Answer: (a) 11.84 Ω; (b) 37.7 mH; (c) 12.5 Ω; (d)
71.3° lagging]
7.
A series R-L circuit of resistance of 25 Ω and inductance of 0.1 H, is connected to
a 250-V, 50-Hz, supply. Calculate the (a) inductive reactance, (b) impedance, (c) current,
(d) voltage across the resistive component, (e) voltage across the inductive component,
(f) phase angle. [Answer: (a) 31.42 Ω; (b) 40.13 Ω; (c) 6.23 A; (d) 156 V; (e) 196 V; (f)
51.5° lagging.]
8.
A series R-L circuit of resistance 15 Ω and inductance 0.08 H, is connected across
a 240-V, 50-Hz, supply. Calculate the (a) reactance, (b) impedance, (c) current, (d)
voltage across the resistive component, (e) voltage across the inductive component, (f)
phase angle. [Answer: (a) 25.12 Ω; (b) 29.3 Ω; (c) 8.19 A; (d) 122.85 V; (e) 205.73 V;
(f) 59.2° lagging]
9.
A current of 4.8 A results when a 30-Ω resistor is connected in series with a
capacitor, across a 240-V, 50-Hz, supply. Find (a) the circuit’s impedance, (b) the
capacitance of the capacitor, and (c) the circuit’s phase angle. [Answer: (a) 50 Ω; (b)
79.6 μF; (c) 53.13° leading]
10.
A series circuit has a resistance of 5 Ω, an inductance of 74 μH, and a capacitance
of 338 pF. What is the resonant frequency of the circuit? {Answer: 1 MHz]
11.
A 5 μF capacitor and a coil are connected in series circuit which is then found to
resonate at 50 MHz. What is the inductance of the coil? [Answer: 2.02 μH]
12.
A circuit consists of a 40-Ω resistor, an inductor of 0.5 H, and a variable
capacitor, all connected in series, across a 100-V, 50-Hz, supply. What value of
capacitance will cause the circuit to resonate, and what will be the voltage drops across
the inductor and the capacitor at resonance? [Answer: 20.2 μF; 393 V; 393 V]