# 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. - Physics

Sum

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?

#### Solution

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.

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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 10 Electric Current in Conductors
Q 27 | Page 199