Six similar bulbs are connected as shown in the figure with a DC...

Case (i): When all bulbs are glowing, then,

${R}_{eq} = \dfrac{2}{3}R$

Then, initially power consumption will be from the equation,

Power $P = \dfrac{{E}^{2}}{R}$

${P}_{i} = \dfrac{{E}^{2}}{{R}_{eq}} = \dfrac{3{E}^{2}}{2R} . . .$\left(1\right)$</p><p>Case (ii): When two bulbs in section$A$and one bulb in the section are glowing, <br /><img src="https://cdn-question-pool.Quantrex.app/pyq/neet/c50204ff-0315-4844-a030-df8958795fea-image.png" style="width: 283px; height: 170px;" /><br />${R}_{eq}^{'} = \dfrac{R}{2} + R = \dfrac{3}{2}R$<br />${P}_{f} = {E}^{2}{R}_{eq}^{'} = \dfrac{2{E}^{2}}{3R} . . . \left(2\right)$</p><p>From above two equations, ratio of power is, </p><p>$\dfrac{{P}_{i}}{{P}_{f}} = \dfrac{9}{4}