Question

A bulb is made using two filaments. A switch selects whether the filaments are used individually or in parallel. When used with a 15 V battery, the bulb can be operated at 5 W, 10 W or 15 W. What should be the resistances of the filaments?

Answer 1

We know:-

\[R = \frac{V^2}{P}\]

where R is the resistance, V is the voltage drop and P is the power on which the bulb is operated.

We can calculate the resistance of the bulb for the same V and different P.

The resistances of the bulb for three different powers are:-

\[R_1  = \frac{\left( 15 \right)^2}{5} = 45  \Omega\]

\[ R_2  = \frac{\left( 15 \right)^2}{10} = 22 . 5  \Omega\]

\[ R_3  = \frac{\left( 15 \right)^2}{15} = 15  \Omega\]

When the two resistance are used in parallel, the equivalent resistance will be less than their individual resistance.

∴ The two resistance are 45 Ω and 22.5 Ω.