Question

An alternating current is given by \( i = (3 \sin \omega t + 4 \cos \omega t) \) A. The rms current will be:

• A. \( \frac{7}{\sqrt{2}} \) A
• B. \( \frac{1}{\sqrt{2}} \) A
• C. \( \frac{5}{\sqrt{2}} \) A
• D. \( \frac{3}{\sqrt{2}} \) A

Hint:

The RMS value of an alternating current is found using the square root of the sum of squares of coefficients in sine and cosine components.

Answer 1

The Correct Option is C

Step 1: Use RMS Current Formula For an alternating current of the form: \[ i = A \sin \omega t + B \cos \omega t \] The rms value is given by: \[ I_{\text{rms}} = \frac{\sqrt{A^2 + B^2}}{\sqrt{2}} \] where:
- \( A = 3 \),
- \( B = 4 \).
Step 2: Compute \( I_{\text{rms}} \) \[ I_{\text{rms}} = \frac{\sqrt{3^2 + 4^2}}{\sqrt{2}} \] \[ = \frac{\sqrt{9 + 16}}{\sqrt{2}} \] \[ = \frac{\sqrt{25}}{\sqrt{2}} = \frac{5}{\sqrt{2}} \text{ A} \]