Question

A 12W resistor is connected to a battery of 24V. What is the current through the resistor?

• A. \( \frac{1}{\sqrt{2}} \, \text{A} \)
• B. 2 A
• C. \( \sqrt{2} \, \text{A} \)
• D. \( \frac{2}{\sqrt{2}} \, \text{A} \)

Hint:

For resistors, use the power formula \( P = I^2 R \) to calculate the current when the power and resistance are known.

Answer 1

The Correct Option is C

Step 1: Use the formula for electrical power.
The power \( P \) in a resistor is given by: \[ P = I^2 R \] where: - \( P = 12 \, \text{W} \), - \( R = 24 \, \Omega \), - \( I \) is the current.
Step 2: Solve for the current.
Rearranging the formula to solve for \( I \): \[ I = \sqrt{\frac{P}{R}} = \sqrt{\frac{12}{24}} = \sqrt{0.5} = \sqrt{2} \, \text{A} \]
Step 3: Conclusion.
Thus, the current through the resistor is \( \sqrt{2} \, \text{A} \), so the correct answer is (C).