Question

The resistance of an incandescent lamp is
A. Greater when switched off
B. Smaller when switched off
C. Greater when switched on
D. The same whether it is switched off or switched on

Answer 1

Hint:When the electricity is passed through the resistance then it converts the electric energy to the heat energy and light energy as a result the temperature of the resistor increases.

Formula used:
\[\rho = {\rho _0}\left( {1 + \alpha \left( {\Delta T} \right)} \right)\]
Where, \[\rho \] is the final resistivity of material, \[{\rho _0}\] is the initial resistivity of material, \[\alpha \] is the temperature coefficient of the material’s resistivity and \[\Delta T\] is the change in temperature.

Complete step by step solution:
With increase in temperature the resistance increases as the resistivity of the material changes with variation of temperature as,
\[\rho = {\rho _0}\left( {1 + \alpha \left( {\Delta T} \right)} \right)\]
Here \[\rho \] is the final resistivity of material, \[{\rho _0}\] is the initial resistivity of material, \[\alpha \] is the temperature coefficient of the material’s resistivity and \[\Delta T\] is the change in temperature.

When the incandescent lamp is switched off then the electric circuit is not completed and hence there is no flow of electric current through the incandescent lamp. As there is no electric current through the incandescent lamp so there will be no generation of heat and light from the lamp. So the temperature of the incandescent lamp will remain the same as before. Hence, the resistance of the incandescent lamp will be the same.

When the incandescent lamp is switched on then the electric circuit is completed and hence there is flow of electric current through the incandescent lamp. As there is electric current through the incandescent lamp so there will be generation of heat and light from the lamp. So the temperature of the incandescent lamp will increase. Hence, the resistance of the incandescent lamp increases. So, the resistance of the incandescent lamp will be greater when switched on.

Therefore, the correct option is C.

Note: The resistivity of the material of the resistor is directly proportional to the change in temperature and also the resistance is directly proportional to the resistivity of the material. Hence, with increase in temperature the resistance increases.