Question

Consider two lamps A and B of rating 50 W; 220 V and 25 W; 220 V respectively. Find the ratio of the resistances of the two lamps (i.e., R_A : R_B).

Answer 1

Given:

Lamp A: Power P_A = 50 W, Voltage V_A = 220 V 

Lamp B: Power P_B = 25 W, Voltage V_B = 220 V

We need to find the ratio of their resistances.

R_A : R_B = ?

The resistance of a lamp is given by Ohm’s law and the power formula: 

`R = V^2/P`

For Lamp A:

⇒ `R_A = (V_A)^2/P_A`

 ⇒ `R_A = (220)^2/50`

⇒ `R_A = 48400/50`

⇒ R_A = 968 Ω

For Lamp B:

⇒ `R_B = (V_B)^2/P_B`

⇒ `R_B = (220)^2/25`

⇒ `R_B = 48400/25`

⇒ R_B = 1936 Ω

⇒ R_A : R_B = 968 : 1936  ...(Dividing both by 968)

⇒ R_A : R_B = 1 : 2

∴ The ratio of the resistances of the two lamps is 1 : 2.