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 of the cource is

Options

A. 20.0 V
B. 25.6 V
C. 31.9 V
D. 53.5 V

Explanation

To solve the problem, we need to find the total potential difference (V_total) across an AC circuit where the potential differences across an inductance (V_L) and a resistance (V_R) are given.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Potential difference across the inductance (V_L) = 16 V
- Potential difference across the resistance (V_R) = 20 V

2. **Understand the Relationship**:
In an AC circuit with inductance and resistance in series, the total potential difference (V_total) is calculated using the Pythagorean theorem because the voltage across the inductor and the voltage across the resistor are out of phase by 90 degrees.

3. **Apply the Pythagorean Theorem**:
The formula to find the total potential difference is:
\[ V_{total} = \sqrt{V_L^2 + V_R^2} \]

4. **Substitute the Values**:
\[ V_{total} = \sqrt{(16)^2 + (20)^2} \]
\[ V_{total} = \sqrt{256 + 400} \]
\[ V_{total} = \sqrt{656} \]

5. **Calculate the Result**:
\[ V_{total} = \sqrt{656} \approx 25.6 \, \text{V} \]

### Final Answer:
The total potential difference of the source is approximately **25.6 V**.

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