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Question
Compare the power used in the 2 Ω resistor in each of the following circuits:
- a 6 V battery in series with 1 Ω and 2 Ω resistors
- a 4 V battery in parallel with 12 Ω and 2 Ω resistors.
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Solution
(i) Potential difference, V = 6 V
1 Ω and 2 Ω resistors are connected in series. Therefore, equivalent resistance of the circuit is
R = R1 + R2
= 1 + 2
= 3 Ω
current flowing in the circuit Is = `"V"/"R"`
= `6/3`
= 2 A
Since equal electric current flows through all the resistances connected in series,
Therefore, power consumed by a 2 Ω resistor P1 = (I1)2R
= (2)2 × 2
= 8 W
(ii) Here V = 4 V, R1 = 12 Ω
And R2 = 2 Ω
∴ The current flowing through different resistances connected in parallel is different but the potential difference between the ends remains the same.
Therefore, power consumed by a 2 Ω resistor P2 = `"V"^2/"R"`
= `(4 "V")^2/(2 Ω)`
= 8W
Therefore, the 2 Ω resistor will consume the same amount of electrical power in both cases.
i.e., P1 = P2
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