A series battery of `10 ` lead accemulators each of emf `2V` and internal resistor `0.25 ` ohm charged by a `220 V` d.c. mains. To limit the charging circuit a resistance of `47.5 Omega` is used in series in the charging circuit. What is (a) the power applied by the mains and (b) power dissipated as heat ?
(c) Account for the difference of power in (a) and (b)

Answer

`880 W,880 W,880 W,80 W`

Explanation

Effective emf of the battery
`epsilon` internal resistance of battery
`r = 10 xx 2 = 20 V`
Total internal resistance of battery
`r = 10 xx 0.25 Omega`
Total resistance of circuit `= r + R = 2//5 + 47.5= 50.0 Omega`
As the battery emf opposes the charging voltage so effective emf
`V = epsilon = 220 - 20 = 200 V`
Charging current `I = ("Effective emf")/("total resistance") = (V - epsilon)/(r + R) = (200)/(50) = 4 A`
(a) power supplied by the mains
`P_(1) = VI = 220 xx 4 = 880 W`
(b) power dissipated as heat
`P_(2) = l^(2) (R + r) = 4^(2) xx 50 = 800 W`
The difference of power `= P_(1) - P_(2)`
`= 800 - 800 = 80 W`
If is stored in the battery in the from of chemical energy