Question

The energy dissipated per unit time by a wire of resistance \(2R\) connected to a battery of voltage \(2V\) is

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

Hint:

Power formulas: \(P = VI = I^2R = V^2/R\). Choose the one that uses the given quantities.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Energy dissipated per unit time is power. For a resistor, power can be calculated using \(P = \frac{V^2}{R}\).

Step 2: Detailed Explanation:
Given: Resistance of wire, \(R_{wire} = 2R\). Voltage of battery, \(V_{battery} = 2V\). Assuming the wire is connected directly across the battery (no internal resistance mentioned), the power dissipated is: \[ P = \frac{(V_{battery})^2}{R_{wire}} = \frac{(2V)^2}{2R} = \frac{4V^2}{2R} = \frac{2V^2}{R} \]

Step 3: Final Answer:
The energy dissipated per unit time is \(\frac{2V^2}{R}\).