Question

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

• A. 1/60 s
• B. 1/240 s
• C. 1/30 s
• D. 1/120 s

Hint:

A full cycle is $360^\circ$ ($T$). Peak happens at $90^\circ$, which is exactly $1/4$ of the cycle. Therefore, time to peak is always $1/(4f)$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In an alternating current cycle, the current starts from zero, reaches its positive peak, returns to zero, reaches its negative peak, and returns to zero again. The time taken to reach the first peak is one-fourth of the total time period ($T$).

Step 2: Key Formula or Approach:
1. Time Period ($T$) = $1 / f$ 2. Time to reach peak ($t$) = $T / 4$

Step 3: Detailed Explanation:
Given: $f = 60$ Hz. 1. Calculate the total Time Period ($T$): \[ T = \frac{1}{60} \text{ s} \] 2. Calculate the time to reach the peak value (starting from zero): \[ t = \frac{T}{4} = \frac{1/60}{4} \] \[ t = \frac{1}{60 \times 4} = \frac{1}{240} \text{ s} \]

Step 4: Final Answer:
The current takes 1/240 s to reach the peak value.