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Answer :
Final answer:
In the given circuit, the potential difference across the 12 ohm resistor is 10V.
Explanation:
In the given circuit, the 6 ohm and 12 ohm resistors are connected in parallel. This combination is then connected in series with a 10V battery and a 6 ohm resistor. To find the potential difference across the 12 ohm resistor, we need to calculate the equivalent resistance of the parallel combination and the total current flowing through the series combination.
The equivalent resistance of the parallel combination is given by 1/Rp = 1/R1 + 1/R2, where R1 = 6 ohm and R2 = 12 ohm. Plugging in the values, we find Rp = 4 ohm.
To find the total current flowing through the series combination, we use Ohm's law: V = I * R. The total resistance is given by Rtotal = Rs + Rp, where Rs = 6 ohm and Rp = 4 ohm. Plugging in the values, we find Rtotal = 10 ohm. The current flowing through the circuit is then I = V / Rtotal = 10V / 10 ohm = 1A.
The potential difference across the 12 ohm resistor is the same as the potential difference across the parallel combination, which is equal to the potential difference across the series combination. Therefore, the potential difference across the 12 ohm resistor is 10V.
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