JEE MAIN - Physics (2012 - No. 14)
Two electric bulbs marked $$25W$$ $$-$$ $$220$$ $$V$$ and $$100W$$ $$-$$ $$220V$$ are connected in series to a $$440$$ $$V$$ supply. Which of the bulbs will fuse?
Both
$$100$$ $$W$$
$$25$$ $$W$$
Neither
Explanation
The current upto which bulb of marked $$25W$$-$$220V,$$ will
not fuse $${I_1} = {{{W_1}} \over {{V_1}}} = {{25} \over {220}}Amp$$
Similarly, $${I_2} = {{{W_2}} \over {{V_2}}} = {{100} \over {220}}\,Amp$$
The current flowing through the circuit
$$I = {{440} \over {{{\mathop{\rm R}\nolimits} _{eff}}}},\,\,{{\mathop{\rm R}\nolimits} _{eff}} = {R_1} + {R_2}$$
$${R_1} = {{V_1^2} \over {{P_1}}} = {{{{\left( {220} \right)}^2}} \over {25}};\,\,\,$$
$${R_2} = {{V_2^2} \over P} = {{{{\left( {220} \right)}^2}} \over {100}}$$
$$I = {{440} \over {{{{{\left( {220} \right)}^2}} \over {25}} + {{{{\left( {220} \right)}^2}} \over {100}}}}$$
$$ = {{440} \over {{{\left( {220} \right)}^2}\left[ {{1 \over {25}} + {1 \over {100}}} \right]}}$$
$$I = {{40} \over {220}}\,\,Amp$$
as $${I_1}\left( { = {{25} \over {220}}A} \right) < I\left( { = {{40} \over {220}}A} \right) < {I_2}\left( { = {{100} \over {200}}A} \right)$$
Thus the bulb marked $$25W$$-$$220$$ will fuse.
not fuse $${I_1} = {{{W_1}} \over {{V_1}}} = {{25} \over {220}}Amp$$
Similarly, $${I_2} = {{{W_2}} \over {{V_2}}} = {{100} \over {220}}\,Amp$$
The current flowing through the circuit
$$I = {{440} \over {{{\mathop{\rm R}\nolimits} _{eff}}}},\,\,{{\mathop{\rm R}\nolimits} _{eff}} = {R_1} + {R_2}$$
$${R_1} = {{V_1^2} \over {{P_1}}} = {{{{\left( {220} \right)}^2}} \over {25}};\,\,\,$$
$${R_2} = {{V_2^2} \over P} = {{{{\left( {220} \right)}^2}} \over {100}}$$
$$I = {{440} \over {{{{{\left( {220} \right)}^2}} \over {25}} + {{{{\left( {220} \right)}^2}} \over {100}}}}$$
$$ = {{440} \over {{{\left( {220} \right)}^2}\left[ {{1 \over {25}} + {1 \over {100}}} \right]}}$$
$$I = {{40} \over {220}}\,\,Amp$$
as $${I_1}\left( { = {{25} \over {220}}A} \right) < I\left( { = {{40} \over {220}}A} \right) < {I_2}\left( { = {{100} \over {200}}A} \right)$$
Thus the bulb marked $$25W$$-$$220$$ will fuse.
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