Question

A 10-ohm resistor carries a current of 2 A. What is the power dissipated?

• A. 5 W
• B. 10 W
• C. 20 W
• D. 40 W

Hint:

When calculating power in resistors:
- Use \( P = I^2 R \) when current and resistance are known.
- Use \( P = \frac{V^2}{R} \) when voltage and resistance are known.
- Use \( P = VI \) when voltage and current are known.
Always double-check units and remember that power is measured in watts (W).

Answer 1

The Correct Option is D

The power dissipated in a resistor is calculated using standard electric power formulas. The three common formulas for power \( P \) are:

• \( P = I^2 R \)
• \( P = V^2 / R \)
• \( P = VI \)

Given values are:

• Current \( I = 2 \, \text{A} \)
• Resistance \( R = 10 \, \Omega \)

Since voltage is not provided, the most suitable formula is:

\[ P = I^2 R \]

Step 1: Square the current
\[ I^2 = (2 \, \text{A})^2 = 4 \, \text{A}^2 \]

Step 2: Multiply by resistance
\[ P = 4 \times 10 = 40 \, \text{W} \]

Interpretation: The resistor dissipates 40 joules of electrical energy per second, primarily as heat. This represents energy lost due to resistance.

Alternative Method:
First, calculate the voltage across the resistor using Ohm's Law:
\[ V = IR = 2 \times 10 = 20 \, \text{V} \]

Then, apply the formula \( P = VI \):
\[ P = 20 \times 2 = 40 \, \text{W} \]

This calculation confirms the initial result.