Question

A 75-W and a 50-W incandescent light bulbs are designed for use with the same voltage. What is the ratio of the resistance of the 75-W bulb to the resistance of the 50-W bulb

Answer 1

Answer:

The ratio is 0.667.

Explanation:

We are given two incandescent lights which have ratings of 75 W and 50 W .

Both bulbs operate at the same voltage.

The equation of power consumed is given by P = $\frac{V^2}{R}$

Therefore the resistance for the 75 W bulb  = $\frac{V^2}{75}$

Therefore the resistance for the 50 W bulb  = $\frac{V^2}{50}$

Therefore the ratio of the resistance for the 75 W bulb to the resistance of the 50 W bulb is equal to

=  $\frac{\frac{V^2}{75} }{\frac{V^2}{50} }$ = $\frac{V^2}{75} \times \frac{50}{V^{2} } = \frac{50}{75} = \frac{2}{3}$ = 0.667.

The ratio is 0.667.