If the frequency of ac is 60 Hz the time difference corresponding to a phase difference of `60^(@)` is –

Options

A. 60 s
B. 1 s
C. 1/60 s
D. 1/360 s

Answer

To solve the problem of finding the time difference corresponding to a phase difference of 60 degrees when the frequency of the AC is 60 Hz, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between phase difference and time difference**:
The phase difference (\(\Delta \phi\)) is related to the time difference (\(\Delta t\)) by the equation:
\[ \Delta \phi = \omega \Delta t \]
where \(\omega\) is the angular frequency.

2. **Convert the phase difference from degrees to radians**:
The phase difference given is 60 degrees. To convert this to radians:
\[ \Delta \phi = 60^\circ = \frac{60 \times \pi}{180} = \frac{\pi}{3} \text{ radians} \]

3. **Calculate the angular frequency (\(\omega\))**:
The angular frequency is given by:
\[ \omega = 2\pi f \]
where \(f\) is the frequency. Given that \(f = 60 \text{ Hz}\):
\[ \omega = 2\pi \times 60 = 120\pi \text{ radians/second} \]

4. **Rearrange the equation to find the time difference (\(\Delta t\))**:
From the equation \(\Delta \phi = \omega \Delta t\), we can solve for \(\Delta t\):
\[ \Delta t = \frac{\Delta \phi}{\omega} \]

5. **Substitute the values into the equation**:
Substitute \(\Delta \phi = \frac{\pi}{3}\) and \(\omega = 120\pi\):
\[ \Delta t = \frac{\frac{\pi}{3}}{120\pi} \]

6. **Simplify the expression**:
The \(\pi\) in the numerator and denominator cancels out:
\[ \Delta t = \frac{1}{3 \times 120} = \frac{1}{360} \text{ seconds} \]

### Final Answer:
The time difference corresponding to a phase difference of 60 degrees at a frequency of 60 Hz is:
\[ \Delta t = \frac{1}{360} \text{ seconds} \]