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26/09/2021 8:36 pm
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Compare the power used in the 2 Ω resistor in each of the following circuits:
(a) A 6 V battery in series with 1 Ω and 2 Ω resistors, and
(b) A 4 V battery in parallel with 12 Ω and 2 Ω resistors.
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26/09/2021 8:41 pm
(a) Given: Voltage, V= 6 V
Equivalent resistance, R = 1 + 2 = 3 Ω
Current through the circuit,
I = \(\frac{V}{R}\) = \(\frac{6}{3}\) = 2A
∴ Power used, P1 = I2R = (2)2 x 2 = 8W
(b) Since the battery is in parallel with 12 Ω and 2 Ω resistors
∴ Potential difference across 2 Ω resistor,
V = 4V
∴ Power used in 2 Ω resistor, P2 = \(\frac{V^2}{R}\)
= \(\frac{4 \times 4}{2}\)
= 8 W
Now, \(\frac{P_1}{P_2}\) = \(\frac{8W}{8W}\) = 1
Hence, the power used in both the cases is the same.