Consider a battery that has Vt 140 V when it is not connect

Consider a battery that has V_t = 14.0 V when it is not connected to a circuit. When a 10.0 Ohm resistor is connected with the battery, the potential difference across the battery\'s terminals drops to 12.9 V. What is the internal resistance of the battery?

Solution

when it is not connected that mean no current flows in circuit

=> potential difference = E only

=> E = 14 V

now , when it is connected

potential difference = E - ir = 12.9

also i = E/r+10

=> E - Er/r+10 = 12.9

=> 10/r+10 = 12.9/14

=> r + 10 = 140/12.9

=> r = 140/12.9 - 10 = 0.852 ohm ( internal resistance of battery)