Question

Two lamps ‘A’ and ‘B’ of rating 50 W; 220 V and 100 W, 220 V are connected in series combination. Find out the ratio of the resistances (R_A : R_B) of these lamps.

Answer 1

Given: For lamp A:

Power (P_A) = 50 W

Voltage (V_A) = 220 V 

For lamp B:

Power (P_B) = 100 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`

= `(220)^2/50`

= `48400/50`

= 968 Ω

For Lamp B:

⇒ `R_B = (V_B)^2/P_B`

= `(220)^2/100`

= `48400/100`

= 484 Ω

⇒ R_A : R_B = 968 : 484    ...(Dividing both by 484)

= 2 : 1

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