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

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