We need to compare the power consumed in the given two combinations.
A 6 V battery in series with 1 Ohm and 2 Ohm resistors
Potential difference, V = 6 V
1Ohm and 2 Ohm resistors are connected in series.
Therefore, the equivalent resistance of the circuit,
R = 1 + 2 = 3 Ohm
According to Ohm’s law,
V = IR
I is the current through the circuit
I= 6/3 = 2 A
This current will flow through each component of the circuit because there is no division of current in series circuits. Hence, the current flowing through the 2Ohm resistor is 2 A.
Power is given by the expression,
P= I2R =
22X 2 = 8 W
A 4 V battery in parallel with 12 Ohm and 2 Ohm resistors.
Potential difference, V = 4 V
12 Ohm and 2 Ohm resistors are connected in parallel.
The voltage across each component of a parallel circuit remains the same. Hence, the voltage across 2 Ohm resistor will be 4 V.
Power consumed by 2 Ohm resistor is given by
P= V2/R = 42/2 = 8 W
Therefore, the power used by 2 Ohm resistor is 8 W.