Question

Two resistors are connected in parallel, whose resistance values are in the ratio 3:1. Find the ratio of power dissipated.

(a) 1:3

(b) 3:1

(c) 1:2

(d) 2:1

I got this question in a national level competition.

Query is from Combination of Resistors topic in chapter Current Electricity of Physics – Class 12

Answer 1

Right choice is (a) 1:3

For explanation: We can consider the relation that includes power and resistance, i.e.                                      Power = \(\frac {voltage^2}{resistance}\). Since, the resistors are connected in parallel, the voltage across them will be the same. From this relation, power and resistance are inversely proportional to each other.

Thus, \(\frac {P1}{P2} = \frac {R2}{R1} = \frac {1}{3}\)

So, the power dissipated is in the ratio is 1:3.