In an ac circuit the potential differences across an inductance and resistance joined in series are, respectively, 16 V and 20 V. The total potential difference across the circuit is

Options

A. 20 V
B. 25.6 V
C. 31.9 V
D. 53.5 V

Explanation

To find the total potential difference across an AC circuit with a resistor and an inductor connected in series, we can use the following steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Potential difference across the resistor, \( V_R = 20 \, \text{V} \)
- Potential difference across the inductor, \( V_L = 16 \, \text{V} \)

2. **Use the formula for total potential difference**:
In an AC circuit with components in series, the total potential difference \( V \) can be calculated using the formula:
\[ V = \sqrt{V_R^2 + V_L^2} \]

3. **Substitute the values into the formula**:
\[ V = \sqrt{(20 \, \text{V})^2 + (16 \, \text{V})^2} \]

4. **Calculate the squares**:
- \( (20 \, \text{V})^2 = 400 \)
- \( (16 \, \text{V})^2 = 256 \)

5. **Add the squares**:
\[ V = \sqrt{400 + 256} = \sqrt{656} \]

6. **Calculate the square root**:
\[ V \approx 25.6 \, \text{V} \]

7. **Conclusion**:
The total potential difference across the circuit is approximately \( 25.6 \, \text{V} \).

### Final Answer:
The total potential difference across the circuit is \( 25.6 \, \text{V} \).

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