Question

An alternating current is given by $I = 100 \sin(50\pi t)$. How many times will the current become zero in one second?

• A. 25 times
• B. 40 times
• C. 50 times
• D. 100 times

Hint:

- Zeros per cycle = 2 - Total zeros = $2f$

Answer 1

The Correct Option is C

Concept: \[ I = I_0 \sin(\omega t), \quad \omega = 2\pi f \]

Step 1: Find frequency.
\[ \omega = 50\pi = 2\pi f \Rightarrow f = 25\ \text{Hz} \]

Step 2: Zero crossings.
In one cycle, current becomes zero twice.

Step 3: Total in one second.
\[ \text{Number of zeros} = 2f = 2 \times 25 = 50 \]