An alternating voltage voltage source is connected, in an A.C. circuit whose maximum value is 170 volt. The value of potential at a phase angle of `45^(@)` will be –

Options

A. 120.20 Volt
B. 110.12 Volt
C. 240 Volt
D. Zero

Answer

To find the value of potential at a phase angle of 45 degrees for an alternating voltage source with a maximum value of 170 volts, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Maximum Voltage (V₀)**:
The maximum voltage (V₀) is given as 170 volts.

2. **Understand the Formula for Instantaneous Voltage**:
The instantaneous voltage (V) in an AC circuit can be expressed as:
\[ V(t) = V₀ \cdot \cos(\phi) \]
where \( \phi \) is the phase angle.

3. **Substitute the Given Phase Angle**:
We need to find the voltage at a phase angle of \( \phi = 45^\circ \). Therefore, we can write:
\[ V = V₀ \cdot \cos(45^\circ) \]

4. **Calculate the Cosine of the Angle**:
The cosine of 45 degrees is:
\[ \cos(45^\circ) = \frac{1}{\sqrt{2}} \approx 0.7071 \]

5. **Substitute the Values into the Formula**:
Now we can substitute the values into the equation:
\[ V = 170 \cdot \cos(45^\circ) = 170 \cdot \frac{1}{\sqrt{2}} \]

6. **Calculate the Result**:
To find the value of V:
\[ V = 170 \cdot \frac{1}{\sqrt{2}} \approx 170 \cdot 0.7071 \approx 120.21 \text{ volts} \]

7. **Round the Result**:
We can round this value to:
\[ V \approx 120.2 \text{ volts} \]

### Final Answer:
The value of potential at a phase angle of 45 degrees is approximately **120.2 volts**.

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