Question

If R1 and R2 are the two resistances of filaments of a 400 W and a 200 W lamp, designed to operate on same voltage , then
A) R1= 2R2
B) R2 = 2R1
C) R2 = 4R1
D) R1 = R2

Answer 1

Answer:

A is the correct answer

Answer 2

$\bf{\underline{\underline{Question}}}$

If R1 and R2 are the two resistances of filaments of a 400 W and a 200 W lamp, designed to operate on same voltage , then

A) R1= 2R2

B) R2 = 2R1

C) R2 = 4R1

D) R1 = R2

$\:$

$\bf{\underline{\underline{Step\:by\:step\:Solution}}}$

$\:$

$\bf{As\:we\:know\:\:,}$

$\:$

$\bf{Power\:of\:bulb\:is\:given\:by:-}$

$\:$

$\bf{P\:=\:{\frac{v^{2}}{R}}}$

$\:$

$\bf{Case\:1\:,}$

$\:$

$\bf{400\:=\:{\frac{v^{2}}{R_{1}}}}\:$

$\:$

$\bf{Similarly\:}$

$\:$

$\bf{Case\:2\:,}$

$\:$

$\bf{200\:=\:{\frac{v^{2}}{R_{2}}}}\:$

$\:$

$\bf{Dividing\:both\:Cases\:,}$

$\:$

$\bf{\cancel\frac{400}{200}}$=$\bf{\frac{\cancel v^{2}}{R1}}\times{\frac{R2}{\cancel v^{2}}}$

$\:$

$\bf{2\:=\: {\frac{R_{2}}{R_{1}}}}$

$\:$

$\bf{\frac{R_{1}}{R_{2}}}={\frac{1}{2}}$

$\:$

$\bf{Hence\:}$

$\:$

$\bf{R_{1}}:{R_{2}}={1}:{2}$

$\:$

$\bf{Option\:A\: is\: correct}$

$\:$

$\bf{\underline{\underline{Thanks}}}$