Example of thermal and chemical effect of current
Example: twenty one electric bulb are connected in series with the mains of a 220 V supply. After one bulb is fused, the remaining 20 bulbs are again connected in series across the same main. By what percentage will the illumination of (i) a bulb change (ii) all the bulbs change?
Solution: Let R be the resistance of each bulb.
Total resistance of all the 21 bulbs in series = 21 R.
Therefore, current I = 220/(21R)
Illuminating power of each bulb,
P = I2R=(220/21R)2 ×R = (220/21)2 × 1/R
Illuminating power of all the bulbs,
P’ =(220/21R)2 × 21 R = (220)2/21R
When one bulb is fused, then current,
I’ =220/20R
Now illuminating power of each bulb,
P’ =(220/20R)2×R = (220/20)2 × 1/R
Illuminating power of all the bulbs,
P’ = (220/20R)2 × 20R= (220)2/20R
(i) % increases in illuminating power of one bulb
= (p’ –p)/p × 100 = [(p’/p )-1] × 100
= [(220)2/(20)2 R/ (220)2/(21)2 R -1] × 100= 10.25 %
(ii) % increase in illumination of all the bulbs
= [(p’ – p)/p ]× 100 =[(p’/p)-1] × 100
=({ [(220)2/20R]/[(220)2/21 R]} -1) × 100 = 5%
Ans : 5%