The peak value of an alternating current is 5A and its frequency is 60Hz. The rms value and the time taken by current take to reach the peak value starting from zero is:

Options

A. `3.5` A, `(1/240)` s
B. `3.5` A, `(1/360)` s
C. `35` A, `(1/240)` s
D. `4.0` A, `(1/240)` s

Explanation

To solve the problem step by step, we will find the RMS value of the alternating current and the time taken to reach the peak value from zero.

### Step 1: Calculate the RMS Value
The RMS (Root Mean Square) value of an alternating current is given by the formula:

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

where \(I_0\) is the peak value of the current.

Given:
- Peak value \(I_0 = 5 \, \text{A}\)

Substituting the value into the formula:

\[ I_{\text{rms}} = \frac{5}{\sqrt{2}} \approx \frac{5}{1.414} \approx 3.54 \, \text{A} \]

### Step 2: Calculate the Time Period
The frequency \(f\) is given as 60 Hz. The time period \(T\) is the reciprocal of the frequency:

\[ T = \frac{1}{f} = \frac{1}{60} \, \text{s} \]

### Step 3: Calculate the Time to Reach Peak Value
The current reaches its peak value at a quarter of the time period. Therefore, the time taken to reach the peak value from zero is:

\[ t = \frac{T}{4} = \frac{1/60}{4} = \frac{1}{240} \, \text{s} \]

### Final Answers
- RMS Value: \(I_{\text{rms}} \approx 3.54 \, \text{A}\)
- Time to reach peak value: \(t = \frac{1}{240} \, \text{s}\)