A resistor and an inductor are connected to an ac supply of 120 V and 50 Hz, the current in the circuit is 3 A. If the power consumed in the circuit is 108 W, then the resistance in the circuit is

Options

A. (A) `12 Omega`
B. (B) `40 Omega`
C. (C) `sqrt((52 xx 28))Omega`
D. (D) `360 Omega`

Explanation

To find the resistance in the circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Voltage (V) = 120 V
- Frequency (f) = 50 Hz (not directly needed for this calculation)
- Current (I) = 3 A
- Power (P) = 108 W

2. **Understand the Power Consumption in the Circuit:**
- In an AC circuit with a resistor and an inductor, the power consumed is primarily due to the resistor. The inductor does not consume power; it only stores energy temporarily.

3. **Use the Power Formula:**
- The power consumed in a resistive circuit can be calculated using the formula:
\[ P = I \times V_{\text{RMS}} \]
- However, since we are interested in finding resistance, we can rearrange the formula to express power in terms of resistance:
\[ P = I^2 \times R \]

4. **Rearranging the Formula to Find Resistance:**
- From the equation \( P = I^2 \times R \), we can solve for resistance \( R \):
\[ R = \frac{P}{I^2} \]

5. **Substituting the Known Values:**
- Now, substitute the values of power and current into the equation:
\[ R = \frac{108 \, \text{W}}{(3 \, \text{A})^2} \]

6. **Calculating the Resistance:**
- Calculate \( I^2 \):
\[ (3 \, \text{A})^2 = 9 \, \text{A}^2 \]
- Now substitute this back into the equation for resistance:
\[ R = \frac{108 \, \text{W}}{9 \, \text{A}^2} = 12 \, \Omega \]

7. **Final Answer:**
- The resistance in the circuit is \( R = 12 \, \Omega \).