question_answer

Two electric bulbs marked 25W - 220 V and 100 W - 220V are connected in series to a 440 V supply. Which of the bulbs will fuse?

A) Both                

B)        100 W

C) 25 W    

D)        Neither

Correct Answer: C

Solution :

The current upto which bulb of marked 25 W-220 V, will not fuse \[{{I}_{1}}=\frac{{{W}_{1}}}{{{V}_{1}}}=\frac{25}{220}\,\,Amp\] Similarly, \[{{I}_{2}}=\,\,\frac{{{W}_{2}}}{{{V}_{2}}}=\frac{100}{220}\,\,Amp\] The current flowing through the circuit \[I=\frac{440}{{{\operatorname{R}}_{eff}}}\] \[{{\operatorname{R}}_{eff}}={{R}_{1}}+{{R}_{2}}\] \[{{\operatorname{R}}_{1}}=\,\,\frac{V_{1}^{2}}{{{P}_{1}}}=\frac{{{(220)}^{2}}}{25};\,\,\,{{R}_{2}}=\frac{V_{2}^{2}}{P}=\frac{{{(220)}^{2}}}{100}\] \[I=\frac{440}{\frac{{{(220)}^{2}}}{25}+\frac{{{(220)}^{2}}}{100}}=\frac{440}{{{(220)}^{2}}\left[ \frac{1}{25}+\frac{1}{100} \right]}\] \[I=\frac{40}{220}Amp\] \[\because \,\,{{I}_{1}}\left( =\frac{25}{220}A \right)<I\left( \frac{40}{220}A \right)<{{I}_{2}}\left( =\frac{100}{200}\,A \right)\]