Resistance and Power

Resistance (R) is a measure of how much a component opposes the flow of electric current. It is measured in ohms (Ω). Power (P) is the rate at which work is done or energy is transferred per unit time. It is measured in watts (W).

Power Formula

The power (P) in an electrical circuit can be calculated using the formula:

P = V^2 / R

Where P is the power in watts, V is the voltage in volts, and R is the resistance in ohms.

Given Information

Two light bulbs are marked 230 V; 75 W and 230 V; 150 W. This means that both bulbs have the same voltage of 230 V, but different power ratings of 75 W and 150 W.

Let's assume the resistance of the first bulb is R. We need to find the resistance of the second bulb.

Using the power formula, we can rearrange it to solve for resistance:

R = V^2 / P

Resistance of the First Bulb

For the first bulb with a power rating of 75 W, we can plug in the values:

R = (230 V)^2 / 75 W

Calculating this, we find:

R ≈ 710.67 ohms

Resistance of the Second Bulb

We are given that the second bulb also has a voltage of 230 V, but a power rating of 150 W. Let's assume the resistance of the second bulb is R2.

Using the power formula again, we can set up the following equation:

R2 = (230 V)^2 / 150 W

Calculating this, we find:

R2 ≈ 353.33 ohms

Comparison of Resistances

To find the relationship between R and R2, we can divide the equation for R2 by the equation for R:

R2 / R = [(230 V)^2 / 150 W] / [(230 V)^2 / 75 W]

Simplifying this expression, we get:

R2 / R = (75 W) / (150 W)

R2 / R = 1/2

Therefore, the resistance of the second bulb (R2) is half the resistance of the first bulb (R). Hence, the correct answer is option B, (1/2)R.