A coil has an inductance of `22/pi H` and is joined in series with a resistance of `220 Omega`.When an alternating `e.m.f` of `220 V` at `50 c.p.s` is applied to it.then the wattless component of the `rms` current in the circuit is

Options

A. `5` ampere
B. `0.5` ampere
C. `0.7` ampere
D. `7` ampere

Explanation

To solve the problem, we need to find the wattless component of the RMS current in the circuit. The wattless component refers to the reactive current, which is associated with the inductance in the circuit.

### Step-by-Step Solution:

1. **Given Data**:
- Inductance \( L = \frac{22}{\pi} \, \text{H} \)
- Resistance \( R = 220 \, \Omega \)
- Voltage \( V = 220 \, \text{V} \)
- Frequency \( f = 50 \, \text{Hz} \)

2. **Calculate the Inductive Reactance \( X_L \)**:
\[ X_L = 2 \pi f L \]
Substituting the values:
\[ X_L = 2 \pi (50) \left(\frac{22}{\pi}\right) = 2 \times 50 \times 22 = 2200 \, \Omega \]

3. **Calculate the Impedance \( Z \)**:
The total impedance \( Z \) in a series circuit with resistance and inductance is given by:
\[ Z = \sqrt{R^2 + X_L^2} \]
Substituting the values:
\[ Z = \sqrt{(220)^2 + (2200)^2} = \sqrt{48400 + 4840000} = \sqrt{4888400} \approx 2200.91 \, \Omega \]

4. **Calculate the RMS Current \( I \)**:
The RMS current can be calculated using Ohm's law:
\[ I = \frac{V}{Z} \]
Substituting the values:
\[ I = \frac{220}{2200.91} \approx 0.1 \, \text{A} \]

5. **Calculate the Wattless Component of the Current**:
The wattless component (reactive current) is given by:
\[ I_{wattless} = \frac{V}{X_L} \]
Substituting the values:
\[ I_{wattless} = \frac{220}{2200} = 0.1 \, \text{A} \]

### Final Answer:
The wattless component of the RMS current in the circuit is \( 0.1 \, \text{A} \).

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