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
Correct answer: (c) 1 : 4
Explanation:
Since the two wires have same material, length and diameter, they have the same resistance. Let the resistance of each wire be R.
Let applied potential difference be V.
Rseries = R1 + R2
= R + R = 2R
Pseries = \(\frac{V^2}{R_{series}}\)
= \(\frac{V^2}{2R}\) ......(i)
\(\frac{1}{R_{parallel}}\) = \(\frac{1}{R_1}\) + \(\frac{1}{R_2}\)
Rparallel = \(\frac{R}{2}\)
Pparallel = \(\frac{V^2}{R_{parallel}}\)
= \(\frac{2V^2}{R}\) .......(ii)
Dividing (ii) from (i),
\(\frac{P_{series}}{P{parallel}}\) = \(\frac{1}{4}\)