In L-R circit, the A.C. source has voltage `220V`. If potential difference across inductor is `176V`, the potential difference across the resistor (in Volts) is `Kxx33`. Find the value of `K`

Explanation

To solve the problem step by step, we need to use the relationship between the voltages in an L-R circuit. The total voltage (V) across the circuit is related to the voltages across the inductor (V_L) and the resistor (V_R) by the following equation:

1. **Write down the known values:**
- Total voltage (V) = 220 V
- Voltage across the inductor (V_L) = 176 V

2. **Use the formula for the voltages in an L-R circuit:**
\[ V^2 = V_R^2 + V_L^2 \]
Here, \(V_R\) is the voltage across the resistor.

3. **Rearrange the formula to find \(V_R\):**
\[ V_R^2 = V^2 - V_L^2 \]

4. **Substitute the known values into the equation:**
\[ V_R^2 = 220^2 - 176^2 \]

5. **Calculate \(220^2\) and \(176^2\):**
\[ 220^2 = 48400 \]
\[ 176^2 = 30976 \]

6. **Subtract the squares:**
\[ V_R^2 = 48400 - 30976 = 17424 \]

7. **Take the square root to find \(V_R\):**
\[ V_R = \sqrt{17424} \approx 132 \text{ V} \]

8. **Set up the equation for \(V_R\):**
We know from the problem that \(V_R = K \times 33\).
\[ 132 = K \times 33 \]

9. **Solve for \(K\):**
\[ K = \frac{132}{33} = 4 \]

10. **Conclusion:**
The value of \(K\) is 4.