$(a)$ State the commercial unit of electric energy and find its relation with its $SI$ unit.
$(b)$ The current through a resistor is made three times its initial value. Calculate how it will affect the heat produced in the resistor.
$(c)$ Find the increase in the amount of heat generated in a conductor if another conductor of double resistance is connected in the circuit,keeping all other factors unchanged.

(N/A) The commercial unit of electric energy is kilowatt-hour $(kWh)$.
The $SI$ unit of electrical energy is Joule $(J)$.
$1 \, kWh = 1000 \, W \times 3600 \, s = 3.6 \times 10^6 \, J$.
$(b)$ According to Joule's law of heating,$H = I^2Rt$.
If the current $I$ becomes $3I$,the new heat $H' = (3I)^2Rt = 9I^2Rt = 9H$.
Thus,the heat produced will become nine times the initial value.
$(c)$ Initial heat $H = I^2Rt$.
If the resistance $R$ is replaced by a conductor of double resistance $(2R)$,the new heat $H' = I^2(2R)t = 2I^2Rt = 2H$.
Thus,the heat produced will become twice the initial value.