Question 4:

Two conducting wires of the same material and of equal lengths and equal

diameters are first connected in series and then parallel in a circuit across the

same potential difference. The ratio of heat produced in series and parallel

combinations would be −

(a) 1:2

(b) 2:1

(c) 1:4

(d) 4:1

Answer:

(c) Heat produced in the circuit is inversely proportional to the resistance R.

Let R_S and R_P be the equivalent resistances of the wires if connected in series

and parallel respectively. Hence, for same potential difference V, the ratio of

heat produced in the circuit is given by

Where,

Heat produced in the series circuit = H_S

Heat produced in the parallel circuit = H_P

Equivalent resistance, R_S = R + R = 2R

Equivalent resistance,

Therefore, the ratio of heat produced in series and parallel combinations is 1:4.

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