Question

The r.m.s value of current in a 50 Hz A.C. circuit is 10 A. The average value of A.C. current over a cycle is

• A. Zero
• B. 10 A
• C. 7.072 A
• D. 14.14 A

Hint:

A sinusoidal current is positive for half the cycle and negative for the other half, so its average over a full cycle cancels.

Answer 1

The Correct Option is A

Step 1: Symmetry
The positive and negative half-cycles have equal areas, so they cancel exactly.

Step 2: Why the other options fail
10 A is the r.m.s. value. $7.072\ \text{A}$ is $\frac{10}{\sqrt{2}}$, which is not an average over a full cycle. $14.14\ \text{A}$ is the peak value.

Step 3: Result
Hence the average over a full cycle is zero.

Final Answer:
The average value of current over a cycle is zero. \[ \boxed{\text{(A) }\text{Zero}} \]