# Numerical Problems : Alternating Current

#### LEVEL – I

Q:1. If the voltage in an ac circuit is represented by the equation, v = 220√2 sin(314t – φ) V .

Calculate (a) peak and rms value of the voltage (b) average voltage (c) frequency of AC.

Ans: (a) 311 V, 220 V (b) 0 (c) 50 Hz

Q:2. Find the maximum value of current when inductance of two henry is connected to 150 V , 50 cycle supply ?

Ans: $\displaystyle \frac{3}{2\sqrt{2}\pi} A$

Q:3. A coil of resistance 300 Ω and inductance 1.0 henry is connected across an alternately voltage of frequency 300/2π Hz. Calculate the phase difference between the voltage and current in the circuit.

Ans: $\displaystyle \frac{\pi}{4}$

Q:4. A 0.21 H inductor and a 12Ω resistance connected in series to a 220 V, 50 Hz ac source. Calculate the current in the circuit and the phase angle between the current and the source voltage.

Ans: 3.28 A , 79.7°

Q:5. A capacitor of 10μF and an inductor of 1 H are joined in series. An ac of 50 Hz is applied to this combination. What is the impedance of the combination ?

Ans: 4.47 Ω

Q:6. A coil has a inductance of 1 henry.

(a) At what frequency will it have a reactance of 3142 Ω ?

(b) What should be the capacity of a condenser which has the same reactance at that frequency?

Ans: (a) 500 Hz. (b) 0.11 μF

Q:7. A 100 mH inductor , a 25 μF capacitor and a 15 Ω resistor are connected in series to a 120 V, 50 Hz a.c. source. Calculate

(a) impedance of the circuit at resonance.

(b) current at resonance.

(c) Resonant frequency.

Ans: (a) 15 Ω (b) 8 A (c) 100.7 Hz

Q:8. Find the value of an inductance which should be connected in series with a capacitor of 5μF, a resistance of 10Ω and an ac source of 50 Hz so that the power factor of the circuit is unity.

Ans: $\displaystyle \frac{20}{\pi^2}$

Q:9. A voltage of 10V and frequency 1000 Hz is applied to a 0.1μF capacitor in series with a resistor of 500 Ω. Find the power factor of the circuit and the average power dissipated.

Ans: (a) PF = 0.3 , PAV = 0.018 W

Q: 10. The inductance of a choke-coil is 0.2 henry and its resistance is 0.50 Ω . If a current of 2.0 ampere (rms value) and frequency 50Hz be passed through it, what will be the potential difference across its ends ?

Ans: 125.6 V

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