Question

A signal of \( v = 5 + 10 \sin \omega t \) is applied across a \( 2\, \Omega \) resistor. The power dissipated in the resistor is

• A. \( 75\, W \)
• B. \( 37.5\, W \)
• C. \( 62.5\, W \)
• D. \( 125\, W \)

Hint:

When both DC and AC voltages are present, calculate power for each separately and add them for total power.

Answer 1

The Correct Option is B

Given: \[ v = 5 + 10 \sin \omega t \] The total power is the sum of DC and AC power components. - DC component: \[ P_{DC} = \frac{V_{DC}^2}{R} = \frac{5^2}{2} = 12.5\, W \] - AC component: \[ P_{AC} = \frac{(V_{m}/\sqrt{2})^2}{R} = \frac{(10/\sqrt{2})^2}{2} = \frac{(100/2)}{2} = 25\, W \] Total power: \[ P_{total} = 12.5 + 25 = 37.5\, W \]