Question

What will happen when a $40watt,$ $220volt$ lamp and $100watt,$ $220volt$ lamp are connected in series across $40volt$ supply?

• A. Neither lamp will fuse
• B. $40watt$ lamp will fuse
• C. $100watt$ lamp will fuse
• D. Both lamps will fuse

Answer 1

The correct option is A Neither lamp will fuse

Step 1: Current rating of first lamp
Given $P_1=40W,V_1=220V$
$l_1=\frac{P_1}{V_1}=\frac{40}{220}=\frac{2}{11}A=0.18A$
Also $\Rightarrow R_1=\frac{V_1^2}{P_1}=\frac{220\times 220}{40}=1210\Omega$

Step 2:Current rating of second lamp
Given $P_2=100W,V_2=220V$
$\Rightarrow l_2=\frac{P_2}{V_2}=\frac{100}{220}=\frac{5}{11}A=0.45A$
Also $\Rightarrow R_2=\frac{V_2^2}{P_2}=\frac{220\times 220}{100}=484\Omega$
Step 3: Find total current in series combination
Let the current flowing through them be. $I.$
In series combination, equivalent resistance is given by:
$R=R_1+R_2$
$\therefore l=\frac{V}{R_1+R_2}$
Given $V=40V$
Then $\Rightarrow l=\frac{40}{1210+484}=\frac{40}{1694}=0.0236A$
Thus, the current flowing through both the bulbs is lesser than their current ratings.
Hence, neither of the bulbs will fuse.
$\therefore$ option $\left(d\right)$ is correct.