When a 209ohm resistor is connected across the terminals of

When a 20.9-ohm resistor is connected across the terminals of a 12.0-V battery, the voltage across the terminals of the battery falls by 0.23 V. What is the internal resistance of this battery? (Give your answer to the nearest 0.001-ohm).

Solution

Voltage drop across internal resistance is

V_r=0.23 Volts

From Voltage divider rule

V_r=E*(r/20.9+r)

0.23=12*(r/20.9+r)

4.807+0.23r =12r

11.77r=4.807

r=0.4084 ohms =0.408 ohms(approx)