Question

Six similar bulbs are connected as shown in the figure with a DC source ofemfE, 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 :
(1) 4:9
(2) 9:4
(3) 1:2
(4) 2:1

Answer 1

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 9:4

Step by step explanation:

The given condition

(i)

All bulbs are glowing:

When six bulbs are connected in a series same amount of current passes through each bulb.

In the given diagram each section have 3 bulbs.

$R_{eq}=\frac{R}{3}+\frac{R}{3}=\frac{2R}{3}$

Power of this series will be

$Power(P_{i})=\frac{E^{2}}{R_{eq}}=\frac{3E^{2}}{2R}...............(1)$

Another condition

(ii)

in the situation when two from section A and one from section B are glowing

$R_{eq}=\frac{R}{2}+R=\frac{3R}{2}$

$Power_({f})=\frac{2E^{2}}{3R}$........................(2)

The ratio of equation (1) and (2) is

               $\frac{p_{i}}{p_{f}}=\frac{\frac{3E^{2}}{2R}}{\frac{2E^{2}}{3R}}$

                  $\Rightarrow \frac{3E^{2}\,3R}{2R\,2E^{2}}$

                  $\Rightarrow 9:4$

Therefore,  ratio of power consumption will be 9:4

Hence, correct option - 2