question_answer

What will happen when a 40 W, 220 V lamp and 100 W, 220 V lamp are connected in series across 40 V supply?

A)  100 W lamp will fuse

B)  40 W lamp will fuse

C)  Both lamps will fuse

D)  Neither lamp will fuse

Correct Answer: D

Solution :

                When current\[i\]flows, across potential V, then power \[{{v}_{i}}\,,\]and \[V=i\,E\] (Ohms law) The currents required by the two lamps for their normal brightness are \[{{i}_{1}}=\frac{{{p}_{1}}}{{{V}_{1}}}=\frac{40}{220}\]     \[=\frac{2}{11}=0.18\,A\] \[i=\frac{V}{{{R}_{1}}+{{R}_{2}}}\]    \[=\frac{40}{1694}=0.236\] \[{{i}_{2}}=\frac{{{p}_{2}}}{{{V}_{2}}}=\frac{100}{200}=0.45A\] The resistance of the filaments are \[{{R}_{1}}-\frac{V}{{{i}_{1}}}=\frac{220\times 11}{2}=121\,\Omega \]