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When switch is closed, V/3 is recorded and since this is the terminal pd, this is what has been supplied to the series cicuit. This means the internal resistor uses 2/3 V.
Voltages are split based on the resistance of the component.
1/3 V is given to a series circuit with a total resistance of 2 Ohms,
then 2/3 V must have been provided to the internal resistor of 4 ohms.
1/3 V for 2 Ohms
2/3 V for 4 Ohms.