Given :
Voltage of Bulb, V' = 12V
Power of Bulb, P = 36W
Potential of the Cell, V = 20V
To Find :
Resistance Required to Glow the Bulb with Full Intensity.
Resistance of the Given Bulb :
⇒ R₁ = (V')²/P
⇒ R₁ = (12)²/36
⇒ R₁ = 144/36
⇒ R₁ = 4Ω
Current passes through the Bulb :
⇒ I = P/V'
⇒ I = 36/12
⇒ I = 3A
It is a Series Connection. So that, The Current passes through the Whole Circuit is 3A .
Equivalent Resistance R = (R₁ + R₂)
Now, Substituting the Values in Ohm's Law :
⇒ V = IR
⇒ V = I(R₁ + R₂)
⇒ 20 = 3(4 + R₂)
⇒ 3R₂ = 20 - 12
⇒ R₂ = 8/3
⇒ R₂ = 2.67Ω
The Resistance of 2.7Ω is Required to Glow it with Full Intensity.