Under what condition is the heat produced in an electric circuit (a)
directly proportional
(b) inversely proportional to the resistance of the circuit?
Compute the ratio of the total quantitiy of heat produced in the two cases.

Explanation

Expression of heat produced by electric current :
Consider a conductor AB of resistance R.
Let V = PD applied across the ends of AB
I = current flowing through AB.
t = time for which the current is flowing
`:.` Total charge flowing from A to B in time t is q = It. By definition of P.D work done is carrying unit charge from A to B = V.
Total work done in carrying a charge q from A to B is
`W = V xx q = V It = I^(2) Rt`
`( :' V = IR)`
This work done is called electric work done. If this electric work done appears as heat. then amount of heat produced (H) is given by
`H = W = I^(2)` Rt joule.
This is a statement fo joule's law of heating
(a) If same current flows through an electric cirucit, heat is developed. i.e., `H prop R`
(b) If same P.D applied across the electric circuit heat is developed
i.e., `H_(2) prop (1)/(R )`
(c ) The ratio of `H_(1)` and `H_(2)` is given by
`(H_(1))/(H_(2)) = (R )/(1)`
`:. (H_(1))/(H_(2)) = R^(2)`