Compare the power used in the 2 Ohm resistor in each of the following circuits: (i) a 6 V battery in series with 1 Ohm and 2 Ohm resistors, and (ii) a 4 V battery in parallel with 12 Ohm and 2 Ohm resistors.

Answer:

We need to compare the power consumed in the given two combinations.

(i) 6 V battery in series with 1 Ohm and 2 Ohm resistors

A 6 V battery in series with 1 Ohm and 2 Ohm resistors

Potential difference (V) = 6 V

1 Ohm and 2 Ohm resistors are connected in series.

The equivalent resistance of the circuit,

R = 1 + 2

R = 3 Ohm

According to Ohm’s law,

V = IR

Where,
I = Current through the circuit

I= 6/3

I = 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

P = 22× 2

P = 8 W

(ii) 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

P = 42/2

P = 8 W

Therefore, the power used by 2 Ohm resistor is 8 W.

 

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