Question

A frill of 50 bulbs joined in series is connected to mains On getting one bulb fused, the remaining 49 bulbs are again put in series and connected to the same main supply. Will the light emitted by the frill increase or decrease?

Answer 1

Given: frill of 50 bulbs joined in series is connected to mains On getting one bulb fused, the remaining 49 bulbs are again put in series and connected to the same main supply.

To find whether the the light emitted by the frill increase or decrease

Solution:

Let power and voltage of each bulb are $P$ and $V$ respectively.

Then, resistance of each bulb is $R=\frac{V^2}{P}$

Case 1:- When all the bulbs are connected in series then, equivalent resistance of circuit is given by $R_{eq}=R+R+R+.....$ Upto $50$ terms

$R_{eq}=50R=\frac{50V^2}{P}$

current passing through each bulb is $i_1=\frac{E}{R_{eq}}=\frac{E}{\frac{50V^2}{P}}=\frac{PE}{50V^2}$ -----(1)

Here $E$ is the potential difference of circuit.

Case 2:- Now, a bulb is fused. And $49$ bulbs are connected in circuit.

So, equivalent resistance of $49$ bulbs in series combination,

$R_{eq}=R+R+R+....$ Upto $49$ terms

$R_{eq}^{\prime }=49R=\frac{49V^2}{P}$

Current passing each bulb is $i_2=\frac{E}{\frac{49V^2}{P}}=\frac{PE}{49V^2}$ -----(2)

From case 1 and case 2 $i_2>i_1$

e.g., current flow through each bulb is higher than initial.

Means power out put = $i^{2}R$ will be higher

Hence, light emitted by frill increases.