Question

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

• A. 1:2
• B. 2:1
• C. 4 :9
• D. 9:4

Answer 1

Answer: (D)

(i) All bulbs are glowing
$R_{eq}=\frac{R}{3}+\frac{R}{3}=\frac{2R}{3}$
Power $\left(P_i\right)=\frac{E^2}{R_{eq}}=\frac{3E^2}{2R}$ ....(1)
(ii) Two from section A and one from section B are glowing.
$R_{eq}=\frac{R}{2}+R=\frac{3R}{2}$
Power $\left(P_f\right)=\frac{2E^2}{3R}$ .....(2)
$\frac{P_i}{P_f}=\frac{3E^{2}3R}{2R2E^2}=9:4$