Compare the power used in the 2 Ω resistor in each of the following circuits:

(i) a 6 V battery in series with 1 Ω and 2 Ω resistors, and

(ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors.

Asked by Vishal kumar | 2 years ago |  458

1 Answer

Solution :-

(i) The potential difference is 6 V and the resistors 1 Ω and 2 Ω are connected in series, hence their equivalent resistance is given by 1 Ω + 2 Ω = 3 Ω. The current in the circuit can be calculated using the Ohm’s law as follows:

\( I=\frac{V}{R}=\frac{6}{3}=2\,A\)

2. A current will flow across all the components in the circuit because there is no division of current in a series of the circuit.

The power in 2 Ω resistor can be calculated as follows:

\( P=I^2R=(2)^2\times2=8\,W\)

Therefore, the power consumed by the 2 Ω is 8 w

(ii) When 12 Ω and 2 Ω resistors are connected in parallel, the voltage across the resistors remains the same. Knowing that the voltage across 2 Ω resistor is 4 V, we can calculate the power consumed by the resistor as follows:

\( P=\frac{V^2}{R}=\frac{4^2}{2}=8\,W\)

The power consumed by the 2 Ω resistor is 8 W.

Answered by Shivani Kumari | 2 years ago

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