Question

Three identical bulbs B₁, B₂, and B₃ each of power rating 18 W, 12 V are connected to a battery of 12 V.

1. Calculate:
   1. the resistance of each bulb
   2. the current drawn from the cell
2. If the bulb B₃ is removed from the circuit, then will the brightness of the bulb B₁ increase, decrease or remain the same?

Answer 1

a.

1. Power = `("Voltage")^2/"Resistance"`

Resistance = `("Voltage")^2/"Power"`

= `(12 xx 12)/18`

= `144/18`

= 8 ohm

2. `1/R_P = 1/R_2 + 1/R_3`

R_P = `(R_2 xx R_3)/(R_2 + R_3)`

= `(8 xx 8)/(8 + 8)`

= `64/16`

= 4 ohm

Total resistance (R_T) = 8 + 4 = 12 Ω

∴ The current drawn from the cell:

I = `V/R_T`

= `12/12`

= 1 A

b. If B₃ is removed, then total resistance = 8 + 8 = 16 W

The brightness of bulb B decreases due to less current in the circuit.