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 the definition of electric power (\(P\)). The question asks for the power dissipated by a resistor when connected to a voltage source.
Step 2: Key Formula or Approach:
There are three common formulas for electric power (\(P\)):
1. \( P = VI_{source} \)
2. \( P = I^2 R_{wire} \)
3. \( P = \frac{V_{source}^2}{R_{wire}} \)
Since the problem provides the voltage of the battery and the resistance of the wire, the most direct formula to use is the third one.
Step 3: Detailed Explanation:
We are given the following information:
- Resistance of the wire, \(R_{wire} = 2R\).
- Voltage of the battery, \(V_{source} = 2V\).
We need to find the power, \(P\).
Using the formula \( P = \frac{V_{source}^2}{R_{wire}} \):
\[ P = \frac{(2V)^2}{2R} \] Now, let's simplify the expression:
\[ P = \frac{4V^2}{2R} \] \[ P = \frac{2V^2}{R} \] Step 4: Final Answer:
The energy dissipated per unit time (power) is \(\frac{2V^2}{R}\), which corresponds to option (C).