The virtual current of 4 A and 50 Hz flows in an AC circuit contaning a coil. The power consumed in the coil is 240 W. If the virtual voltage across the coil is 100 V, then its resistance will be

Options

A. `(1)/(3pi)Omega`
B. `(1)/(5pi)Omega`
C. `15Omega`
D. `(1)/(pi)Omega`

Answer

To find the resistance of the coil in the given AC circuit, we can use the formula for power consumed in an electrical circuit:

### Step-by-Step Solution:

1. **Identify the given values:**
- Virtual current (I_rms) = 4 A
- Power consumed (P) = 240 W
- Virtual voltage (V) = 100 V

2. **Use the power formula:**
The power consumed in a resistive circuit can be expressed as:
\[ P = I_{rms}^2 \cdot R \]
where \( R \) is the resistance.

3. **Rearrange the formula to solve for resistance (R):**
\[ R = \frac{P}{I_{rms}^2} \]

4. **Substitute the known values into the equation:**
\[ R = \frac{240 \, \text{W}}{(4 \, \text{A})^2} \]

5. **Calculate \( I_{rms}^2 \):**
\[ I_{rms}^2 = 4^2 = 16 \]

6. **Now substitute this back into the equation for R:**
\[ R = \frac{240}{16} \]

7. **Perform the division:**
\[ R = 15 \, \Omega \]

### Final Answer:
The resistance of the coil is **15 Ω**.

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