(i) In the First Case:

Potential difference, V = 6 V

And, Net Resistance, R= 1 + 2 = 3 (Resistors are connected in series)

Now, by Ohm’s law:

Thus, the current flowing in the circuit containing 1 and 2 resistors in series is 2 A. In a series circuit, the same current flows throughout the circuit. So, the current flowing through the 2 resistor is also 2A. Now, we know that the current (in 2 resistor) is 2 A and its resistance is 2 .

Now, Power used in 2 resistor is given as:

(ii) In the Second Case:

Here, 4 V battery is attached across the parallel combination of 12 and 2 resistors, so the potential difference across the 2 resistor will also be 4 V. Because in parallel connection

Voltage is same.

Now, Potential difference, V= 4 V

And Resistance, R = 2

So, Power used in 2 resistor, P= =

Thus, the power used in the 2 resistor in the second case is also 8W.

From both the cases we can say that the 2 resistor uses equal power in both the circuits.