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: Understanding the Question:
We need the peak voltage from \(V = 80 \sin(100\pi t) \cos(100\pi t)\).

Step 2: Key Formula or Approach:
Use trigonometric identity: \(2 \sin A \cos A = \sin 2A\). Thus \(\sin A \cos A = \frac{1}{2} \sin 2A\).

Step 3: Detailed Explanation:
\[ V = 80 \sin(100\pi t) \cos(100\pi t) = 80 \times \frac{1}{2} \sin(200\pi t) = 40 \sin(200\pi t). \] The peak value is the coefficient of the sine function: \(40\ \text{V}\).

Step 4: Final Answer:
Peak voltage = 40 V, option (B).