2019 Current ElectricityCombination of Resistors – Power Dissipation Hard Question 48 of 130 in Current Electricity

Six similar bulbs are connected as shown in the figure with a DC source of emf $E$, and zero internal resistance. The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section B are glowing, will be:

A $4:9$
B $9:4$
C $1:2$
D $2:1$

The answer is B.

Solution

(i) All bulbs glowing: $R_{eq}=\frac{R}{3}+\frac{R}{3}=\frac{2R}{3}$
$P_i=\frac{E^2}{R_{eq}}=\frac{3E^2}{2R}$
(ii) Two from section A and one from section B glowing: $R_{eq}=\frac{R}{2}+R=\frac{3R}{2}$
$P_f=\frac{2E^2}{3R}$
$\frac{P_i}{P_f}=\frac{3E^2}{2R}\times\frac{3R}{2E^2}=\frac{9}{4}$
Ratio $=9:4$

Concept power ratio for different numbers of glowing bulbs

Current Electricity in past papers

130 questions from this chapter have appeared across 27 exam years.