External resistor question?

Question

When an external resistor of resistance R= 28 Ohm is connected to the terminals of a battery, a current of 12.0 Amp flows through the resistor. When an external resistor of resistance R= 128.8 Ohm is connected instead, the current is 4.0 Amp. Calculate:

a) The e.m.f. of the battery and

b) The internal resistance of the battery

Answer 1

case 1, E = IR = 28*12 = 336 volts

case 2, E = 128.8*4 = 515.2 volts

Ri is internal resistance

V = IRi + 336 = 336 + 12Ri

V = IRi + 515.2 = 515.2 + 4Ri

set them equal to each other

336 + 12Ri = 515.2 + 4Ri

8Ri = 179.2

Ri = 22.4 ohms

V = 336 + 12*22.4 = 604.8 volts.

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