Numerical Problems : Alternating Current

LEVEL – I

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.

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

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.

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

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

6. A coil has a inductance of 1 henry.
(a) At what frequency will it have a reactance of 3142Ω?

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

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

(a) impedance of the circuit at resonance.

(b) current at resonance.

(c) Resonant frequency.

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 50Hz so that the power factor of the circuit is unity.

9. A voltage of 10V and frequency 1000Hz 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.

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?

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