The resistance of a 40W car head lamp, drawing current from a 12V battery is ____.

1. Analyze the question

We are given the power ($P$) of a car headlamp as 40W and the voltage ($V$) of the battery as 12V. We need to find the resistance ($R$) of the lamp.

2. Explain the concept

In electricity, the relationship between Power ($P$), Voltage ($V$), and Resistance ($R$) is derived from Ohm’s Law ($V = IR$) and the Power formula ($P = IV$).

By substituting $I = \frac{V}{R}$ into the power formula $P = VI$, we get:

To find the resistance ($R$), we rearrange the formula:

3. Show the solution

• Given: • Power ($P$) = 40 W • Voltage ($V$) = 12 V

• Step-by-step calculation: • Use the formula: $R = \frac{V^2}{P}$ • Substitute the values: $R = \frac{12^2}{40}$ • Calculate the square of the voltage: $12 \times 12 = 144$ • Divide by the power: $R = \frac{144}{40}$ • Simplify: $R = 3.6 \, \Omega$

4. Identify the answer

Comparing our result to the given options, 3.6Ω corresponds to option C.

5. Exam Tip

When dealing with electrical power questions in JAMB, always remember the "Power Triangle": $P = IV$, $P = I^2R$, and $P = \frac{V^2}{R}$. If you are given Voltage and Power, use the formula with $V^2$; if you are given Current and Power, use the formula with $I^2$. This saves you the extra step of calculating the current first!