The peak value of an alternating current is `5 A` and its frequency is `60 Hz`. Find its rms value. How long will the current take to reach the peak value starting from zero?

Options

A. 3.536 A, 4.167 ms
B. 3.536 A, 15 ms
C. 6.07 A, 10 ms
D. 2.536 A, 4.167 ms

Explanation

To solve the problem, we need to find the root mean square (rms) value of the alternating current and the time it takes to reach the peak value starting from zero.

### Step 1: Calculate the rms value of the current

The formula to calculate the rms value (I_rms) from the peak value (I_0) is given by:

\[ I_{rms} = \frac{I_0}{\sqrt{2}} \]

Given that the peak value \(I_0 = 5 \, A\):

\[ I_{rms} = \frac{5 \, A}{\sqrt{2}} \approx \frac{5}{1.414} \approx 3.536 \, A \]

### Step 2: Determine the time taken to reach the peak value

The time period (T) of the alternating current is related to its frequency (f) by the formula:

\[ T = \frac{1}{f} \]

Given that the frequency \(f = 60 \, Hz\):

\[ T = \frac{1}{60} \, s \approx 0.01667 \, s \, (or \, 16.67 \, ms) \]

The current reaches its peak value in a quarter of the time period (T/4):

\[ t = \frac{T}{4} = \frac{1/60}{4} = \frac{1}{240} \, s \approx 0.004167 \, s \, (or \, 4.167 \, ms) \]

### Final Answers:

1. The rms value of the current is approximately \(3.536 \, A\).
2. The time taken to reach the peak value starting from zero is approximately \(4.167 \, ms\).

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