Question

20 identical electric bulbs are connected in series. If one bulb gets fused suddenly and the circuit is reconnected across the same supply then the % change in illumination of all the bulbs is:
(A) 5.26%
(B) 7%
(C) 6.25%
(D) 2.56%

Answer 1

Answer:2.56 percent

Explanation:

Answer 2

Answer:

Percentage change in illumination = 10.80%

Explanation:

Suppose a single bulb has resistance R and the supply is of V volt.

Now we know that,the illumination is directly proportional to the square of the current that is flowing through each bulb.

                $I_1 \propto i_1 ^2$  ....................................................(i)

There are 20 electric bulbs in series and current through each bulb is equal to $i_1$.

    ∴   $i_1 = \frac{V}{20R}$

Using equation (i),we get

       $I_1 \propto (\frac{V}{20R} )^2$

If one bulb gets fused suddenly,then current through each bulb is

$i_2 = \frac{V}{19R}$

       ∴  $I_2\propto (\frac{V}{19R} )^2$

∴ % change in illumination $= \frac{I_2 - I_1}{I_1} *100$  

                                              $= \frac{i_2^2 -i_1^2}{i_1^2}*100$  

                                              $= \frac{\frac{1}{19^2 } - \frac{1}{20^2} }{\frac{1}{20^2} }*100$  

                                              = 10.80 %