A coil of inductance L and negligible resistance is in series with a resistance R. A supply voltage of 40 V (RMS) is connected to them. If a voltage across L is equal to that across R, calculate the voltage across R and the frequency of the supply.

Ans: 28.3 V, 63.7 Hz

An iron-cored coil of inductance 2H and of resistance 500Ω is connected in series with a resistor of 950Ω, and a 220V, 50 Hz ac supply. Find the current flowing in the circuit and the voltage across the coil.

Ans: 0.186 A, 116.87 V

A circuit consists of an inductor of 200 μ H and resistance of 10Ω in series with a variable capacitor and a 0.10V (r.m.s.), 1.0 MHz supply. Calculate (i) the capacitance to give resonance and (ii) the quality factor of the circuit at resonance.

Ans: (i) 1.267 × 10^-10F, (ii) 126

A 50 V a.c. supply is connected to a resistor having resistance 50Ω, in series with a solenoid whose inductance is 0.25H. The potential difference between the ends of the resistor is 25 V. Find the resistance of the wire of the solenoid. Take frequency of the ac source is 50 Hz.

Ans: 11.89 Ω

An iron cored coil of 2 H and 50 Ω resistance placed in series with a resistor of 450 Ω and 200 v, 50 Hz a.c. supply is connected across the arrangement, find

1. the current flowing the coil
2. its phase angle relative to the voltage supply
3. the voltage across the coil.

A.C. mains of 200 volts and 50 Hz is joined to a circuit containing an inductance of 10OmH and a resistance of 20Ω in series. Calculate the power consumed.

Ans: 576.8 watt

A circuit consists of a capacitor of 2μF and a resistor of 1000Ω. An alternating emf of 12V (rms) and frequency 50Hz is applied. Find the current flowing, the voltage across capacitor and the phase angle between the applied emf and current.

Ans: 6.38 × 10^-3 A, 10.2 V, 57.9°

A coil having inductance and resistance is connected to an oscillator giving a fixed sinusoidal output voltage of 5V rms. With the oscillator set at a frequency of 50 Hz, the rms current in the coil is 1A and at a frequency of 100 Hz, the rms current is 0.625A. Determine the inductance of the coil.

Ans: 0.0114 H

L-C-R alternating current series circuit of L = 1H, C = 1 μF and R = 100μ are connected in series with a source of frequency 50Hz. What is the phase shift between current and voltage?

Ans: 88°

An iron-cored coil of inductance 3H arid 50Ω resistance is placed in series with a resistor of 550Ω and a 100 v, 50 Hz ac supply is connected across the arrangements. Find the current flowing in the coil and voltage across the coil.

Ans: 0.09 A, 84.8 V

A coil of inductance 0.1H and negligible resistance is in series with a resistance of 40Ω. A supply voltage of 50 v (rms) is connected to them. If the voltage across L is equal to that across R, calculate the voltage across the inductor and frequency of the supply.

Ans: 63.7 Hz, 35.35 V

An iron cored coil of inductance 2H and resistance 50Ω is connected in series with a resistor of 950Ω. A 220 V, 50 Hz ac supply is connected across the arrangement. Find the current flowing in the circuit and the voltage across the coil.

Ans: 0.186 A, 116.87V

An ac source of 220 V, 50 Hz is connected to a series circuit containing a resistor R and inductor L and a capacitor C. If R = 200 0, L = 0.5 H, and C = 10 μF, calculate,

1. the current in the circuit,
2. the phase angle and
3. the power consumed in the circuit.

Ans: (i) 0.856A (ii) 38.9° (iii) 146.56 Watt

A circuit consists of a capacitor of 2μF and a resistor of 1000Ω. An alternating emf of 12V and frequency 50Hz is applied. Find the voltage across the capacitor and the phase angle between the applied emf and the current.

Ans: 6.37 × 10^-3A, 10.2v, 57.9°

A 100V, 50Hz A.C. source is connected to an LCR circuit containing L = 8.1 mH, C = 12.5 μF and R = 100Ω all are connected in series. Find the p.d. across the resistor.

Ans: 37 V