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The potential difference across the terminals of a battery is 9v when it is discharged with a current of 3A. When the same battery is charged by 2A

current, the potential difference across its terminals is 12v. The emf and internal resistance of the battery is?



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Let the EMF be  E and  Resistance be  R...

When the battery is discharging, then the current is coming out of the  positive terminal.  then the potential across the battery terminals will be:
     V =  E  -  I  R
       9 = E - 3 R        --- (1)

when the battery is charging, then the current goes inside the positive terminal. then :          V = E + I R
                   12 = E + 2 R    --- (2)

   solving them,  5 R = 3    =>  R = 0.6 ohms.

   E = 10.8 Volts or  54/5  Volts.

1 5 1
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