Question

An alternating voltage is represented by \( V = 80 \sin(100\pi t) \cos(100\pi t) \) volt. The peak voltage is

• A. 20 V
• B. 40 V
• C. 30 V
• D. 50 V

Hint:

Whenever you see a product of sine and cosine with the same argument, use the double‑angle identity to simplify and find amplitude.

Answer 1

The Correct Option is B

Step 1: Simplify with an identity.
The product $\sin\theta\cos\theta$ equals $\tfrac12\sin 2\theta$. So the voltage collapses to a single sine.

Step 2: Rewrite the voltage.
\[ V = 80\sin(100\pi t)\cos(100\pi t) = 80\cdot\tfrac12\sin(200\pi t) = 40\sin(200\pi t). \]

Step 3: Identify the peak.
The number in front of the sine is the peak value, which is $40$.

Step 4: State it.
\[ \boxed{40\ \text{V}} \]