# A coil has an inductance of 2.2/pi H and is joined in series with a resistance of 220 ohms. When an alternating emf of 220 volts at 50 cycles per second is applied to it, then the wattless component of the rms current in the circuit is: A 0.5 amperes B 0.7 amperes C 5 amperes D 7 amperes

## Question

A coil has an inductance of $\frac{2.2}{\pi} \mathrm{H}$ and is joined in series with a resistance of $220 \Omega$. When an alternating emf of $220 \mathrm{~V}$ at $50 \mathrm{~c.p.s}$ is applied to it, then the wattless component of the rms current in the circuit is:

A 0.5 $\mathrm{~A}$ B 0.7 $\mathrm{~A}$ C 5 $\mathrm{~A}$ D 7 $\mathrm{~A}$

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## Answer

Question A coil has an inductance of $\frac{2.2}{\pi} \ \mathrm{H}$ and is joined in series with a resistance of $220 \ \Omega$. When an alternating emf of $220 \ \text{V}$ at $50 \ \text{c.p.s}$ is applied to it, then the wattless component of the rms current in the circuit is:

A) 0.5 A

B) 0.7 A

C) 5 A

D) 7 A

The correct answer is **A) 0.5 A**.

Given:

- Inductance, $L = \frac{2.2}{\pi} \ \mathrm{H}$
- Resistance, $R = 220 \ \Omega$
- Alternating emf, $V = 220 \ \text{V}$
- Frequency, $f = 50 \ \text{Hz}$

First, we calculate the inductive reactance, $X_L$: $$ X_L = 2 \pi f L = 2 \pi \cdot 50 \cdot \frac{2.2}{\pi} = 220 \ \Omega $$

Next, we find the impedance, $Z$, of the series circuit: $$ Z = \sqrt{R^2 + X_L^2} = \sqrt{220^2 + 220^2} = 220 \sqrt{2} \ \Omega $$

The rms current, $I$, in the circuit can be given by Ohm's law for AC circuits: $$ I = \frac{V}{Z} = \frac{220}{220 \sqrt{2}} = \frac{1}{\sqrt{2}} \ \text{A} $$

To find the wattless (or reactive) component of the current, $I \sin \phi$, we use the ratio of the inductive reactance to the impedance: $$ I \sin \phi = \frac{V}{Z} \cdot \frac{X_L}{Z} = \frac{220}{220 \sqrt{2}} \cdot \frac{220}{220 \sqrt{2}} = \frac{1}{2} = 0.5 \ \text{A} $$

Thus, the wattless component of the rms current in the circuit is **0.5 A**.

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