Question

A $25$ watt, $220$ volt bulb and a $100$ watt , $220$ volt bulbs are connected in series across $440$ volt line

• A. only $100$ watt bulbs will fuse
• B. only $25$ watt bulbs will fuse
• C. none of these bulbs will fuse
• D. both bulbs will fuse

Answer 1

The correct option is B only $25$ watt bulbs will fuse

we know power rating, $P=\frac{V_0^2}{R}$ where R = Resistance of bulb, given

$R=\frac{V_0^2}{P}$ $V_0=$ Reference 220V in this thin case

own for both bulls :-

$R_1=\frac{V_0^2}{25}$ and $R_2=\frac{V_0^2}{100}$

In series, equivalent resistance :- $R^1=R_1+R_2=V_0^2(\frac{1}{25}+\frac{1}{100})$

$=\frac{V_0^2}{20}$

In, series, current is constant.

So, when connected to supply voltage 440v $(=2v_0),$ current

in the current would be:-

$I=\frac{V}{R^1}=\frac{2v_0}{V_0^2/2_0}=\frac{40}{V_0}$

$\Rightarrow$ Power generated in Bulb 1, $=I^2{R}_1=\frac{{40}^2}{V_0^2}\times \frac{V_0^2}{25}=64w$

and n Bulb 2, $I^2{R}_2=\frac{4_0^2}{V_0^2}\times \frac{V_0^2}{100}=16w$

clearly, $64w>25w\Rightarrow$ only Bulb 1 will blow up.