Question

The filament of a 240 V, 100 W electric lamp heats up from room temperature to its operating temperature. As it heats up, its resistance increases by a factor of 16. What is the resistance of this lamp at room temperature?
A 36Ω
B 580Ω
C 1.5 kΩ
D 9.2 kΩ

Answer 1

240V 100WV^2/R=100->R=V^2/100->R=240^2/100->R=2.4x240->R=24x24->Rcold=24x24/4x4->Rcold=36 ohms A.

Answer 2

We need to use the formula P = IV, where P is the power, I is the current and V is the voltage. 
When we substitute our values in, we get:
100 = 240I, and so I = 0.42 Amps
Now, we have to work out the Resistance in the circuit at the operating temperature.

We do this using the formula V = IR
240 = (100/240) x R, and we get R = 576 Ohms

Since the resistance has gone up by a factor of 16, all we have to do now is to divide this answer by 16 to get the resistance at room temperature.

576/16 = 36 Ohms

Hope I helped!! xx