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

To find the power dissipated in a resistor, we use one of the standard formulas from electric power concepts. The three most common formulas for power \( P \) are: 
1. \( P = I^2 R \) 
2. \( P = V^2 / R \) 
3. \( P = VI \) 
Here, we are given: 
Current \( I = 2 \, \text{A} \) 
Resistance \( R = 10 \, \Omega \) 
We are not given the voltage, so the most convenient formula to use 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 converts 40 joules of electrical energy into heat every second. That’s what we mean by “dissipated power” — energy that’s lost (usually as heat) due to resistance. 
Alternative : 
We can also find the voltage across the resistor using Ohm’s law: 
\[ V = IR = 2 \times 10 = 20 \, \text{V} \] 
Now, apply \( P = VI \): 
\[ P = 20 \times 2 = 40 \, \text{W} \] 
This confirms the same result.