Question

(i) State Joules law of heating and write its mathematical expression.

(ii) Two resistors of resistances 2 and 4 are connected in

a) series

b) parallel

with a battery of given potential difference. Compute the ratio of total quantity of heat produced in the combination in the two cases if the total voltage and time are kept the same for both.

Answer 1

(i) Joule's Law of Heating states that the amount of heat produced in a conductor is directly proportional to the square of the electric current passing through it, the resistance of the conductor, and the time for which the current flows. Mathematically, it can be expressed as 

H = ²Rt

• H is the heat produced (in joules),
• I is the electric current (in amperes),
• R is the resistance of the conductor (in ohms),
• t is the time for which the current flows (in seconds)

(ii) Let the equivalent resistance in series be denoted by R_S and that for parallel be denoted by R_p. Total voltage of the circuit is given by in both cases and the time is denoted by .

• R_s = 2 + 4 = 6 \(\Omega\)
• \(\frac{1}{R_p} = \frac {1}{2} + \frac {1}{4} = \frac {3}{4}, R_p = \frac{4}{3}\)
• H_s = \(\frac{V^2}{R_s} t, H_p = \frac{V^2}{R_p} t\)
• \(\frac{H_s}{H_p} = \frac{R_p}{R_s} = \frac{2}{9}\)