Question

Compare the power used in the 2 12 resistor in each of the following circuits:
(i) a 6 V battery in series with 1 12 and 2 12 resistors, and (ü) a 4 V battery in parallel
with 12 22 and 2 12 resistors.​

Answer 1

Answer:

Potential difference, V = 6 V

1Ohm and 2 Ohm resistors are connected in series. Therefore, equivalent resistance of the circuit, R = 1 + 2 = 3 Ohm

According to Ohm’s law,

V = IR

Where,

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, current flowing through the 2Ohm resistor is 2 A. Power is given by the expression,

P= (I)2R = (2)2 x 2 = 8 W

(ii) 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.

Answer 2

Answer:

Given :-

Potential difference = 6 V

Solution :-

Equivalent resistance = 1 + 2 = 3 Ω

According to the Ohm’s law

V = IR

I = V/R

I = 6/3

I = 2 A

Current through the circuit = 2 A

we know that Power = I²R

P = 2 × 2 × 2

P = 8 W

Hence, the power used by 2 Ω resistor is 8 W.

Answer :- (ii)

Given :-

Potential difference, V = 4 V

Voltage across each component of a parallel circuit remains the same. Then,

Solution :-

P = V²/R

P = 4²/2

P = 8 W

Hence, the power used by 2 Ω resistor is 8 W.