Question

Energy dissipated per unit time by a wire of resistance \(2R\) connected to a 2V battery.

• A. \( \frac{V^2}{2R} \)
• B. \( \frac{V^2}{R} \)
• C. \( \frac{V^2}{4R} \)
• D. \( \frac{V^2}{R} \times 2 \)

Hint:

For power dissipation in a resistor, use the formula \(P = \frac{V^2}{R}\). If the resistance is doubled, the power dissipated is halved.

Answer 1

The Correct Option is C

The energy dissipated per unit time (power) in a resistor can be calculated using the formula: \[ P = \frac{V^2}{R} \] Where: - \(P\) is the power dissipated (energy per unit time), - \(V\) is the voltage across the resistor, - \(R\) is the resistance. However, the question specifies that the resistance is \(2R\), so the formula becomes: \[ P = \frac{V^2}{2R} \] Given that \(V = 2 \, \text{V}\), we substitute \(V = 2\) into the equation: \[ P = \frac{2^2}{2R} = \frac{4}{2R} = \frac{V^2}{4R} \] Thus, the energy dissipated per unit time is \(\frac{V^2}{4R}\).