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Question 12

In the given circuit, the current in resistance $$R_3$$ is:

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Equivalent resistance of the parallel combination of $$R_2$$ and $$R_3$$:

$$R_{23} = \frac{R_2 \times R_3}{R_2 + R_3} = \frac{4 \times 4}{4 + 4} = 2\ \Omega$$

Total equivalent circuit resistance: $$R_{\text{eq}} = R_1 + R_{23} + R_4 = 2 + 2 + 1 = 5\ \Omega$$

Total main loop current: $$I = \frac{V}{R_{\text{eq}}} = \frac{10}{5} = 2\text{ A}$$

$$I_{R_3} = I \times \frac{R_2}{R_2 + R_3} = 2 \times \frac{4}{4 + 4} = 1\text{ A}$$

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