Question

Compare the power used in 2Ω resistor in each of the following cases

(i) A 12 V battery in series with 1Ω and 2Ω resistors.

(ii) A 8 V battery in parallel with 12 Ω and 2Ω resistors.​

Answer 1

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(i)

Given:-

Potential Difference = V = 6 V

Since, 1Ω and 2Ω are connected in series.

Hence, equivalent resistance of the circuit = R = 1Ω + 2Ω = 3Ω

According to Ohm's law,

$\bold{=>V = IR} \\ = > \bold{I = \frac{V}{R} = \frac{6}{3} = 2 A}$

Power used in the 2Ω resistor,

$\bold{Power =I {}^{2} R = 2 {}^{2} \times 2 = \boxed{8W }}$

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(ii)

Given:-

Potential difference = V = 4 V

Since, 12Ω and 2Ω resistors are connected in parallel.

The voltage across each component of a parallel circuit remains the same.

Hence, the voltage across 2Ω resistor will be 4 V.

Power consumed by 2Ω resistor is given by

$\bold{Power = \frac{V {}^{2} }{R} = \frac{4 {}^{2} }{2} = \boxed{8W}}$

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Hope, it helps you.