JEE MAIN - Physics (2019 - 12th January Morning Slot - No. 23)
Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P1 and P2 respectively, then :
P1 = 4W, P2 = 16 W
P1 = 16W, P2 = 4 W
P1 = 9W, P2 = 16 W
P1 = 16W, P2 = 9 W
Explanation
$${R_1} = {{{{220}^2}} \over {25}}$$
$${R_2} = {{{{220}^2}} \over {100}}$$
$$L = {{220} \over {{R_1} + {R_2}}}$$
$${P_1} = {i^2}\,{R_1}$$
$${P_2} = {i^2}\,\,({R_2}\, = \,4W)$$
$$ = {{{{220}^2}} \over {\left( {{{{{220}^2}} \over {25}} + {{{{220}^2}} \over {100}}} \right)}} \times {{{{220}^2}} \over {25}}$$
$$ = {{400} \over {25}} = 16W$$
$${R_2} = {{{{220}^2}} \over {100}}$$
$$L = {{220} \over {{R_1} + {R_2}}}$$
$${P_1} = {i^2}\,{R_1}$$
$${P_2} = {i^2}\,\,({R_2}\, = \,4W)$$
$$ = {{{{220}^2}} \over {\left( {{{{{220}^2}} \over {25}} + {{{{220}^2}} \over {100}}} \right)}} \times {{{{220}^2}} \over {25}}$$
$$ = {{400} \over {25}} = 16W$$
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