Question

An electrical heater is run by a household power supply. If resistance is halved, heat produced is:

• A. halved
• B. same
• C. doubled
• D. quadrupled

Answer 1

The correct option is C doubled

Household power supply is driven by a constant voltage source.

Using ohm's law,

$V=IR$

Since, $R_2=R_1/2\text{and}{V}_2=V_1$

$V_2=I_2{R}_2$

$V_1=I_1{R}_1$

$⟹I_2=2I_1$

By joule's law, heat produced is

$Q=I^{2}Rt$

i.e. $Q_1=I_1^2{R}_{1}t$

$Q_2=I_2^2{R}_{2}t$

$⟹\frac{Q_2}{Q_1}=\frac{I_2^2{R}_2}{I_1^2{R}_1}=2$