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A storage battery of emf 8.0 V and inter...

A storage battery of emf 8.0 V and internal resistance `0.5 Omega` is being charged by a 120V dc supply using a series resistor of `15.5Omega`. what in the terminal voltage of the battery during charging ? What is the purpose of having a series resistor in the charging circuit?

Text Solution

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Net emf in the circuit when the battery of emf 8.0V is charged by a 120V d.c supply is
`E_("net") = E_(2) - E_(1) = 120 - 8.0 = 112.0V`
Current in the circuit during charging will be
`I= (E_("net"))/(R+r)`
Here, `R= 15.5 Omega and r= 0.5 Omega`
`rArr I = (112)/(15.5 + 0.5) = 7A`
For charging the battery, the terminal voltage is given by:
`V= E_(1) = Ir`
`=8+7 xx 0.5 =8 + 3.5 = 11.5V`
The series resistor helps in limiting the current drawn from the external source because if it is not present, the current drawn from the source will be high and can exceed the maximum allowed current in the battery being charged.
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