In the circuit diagram shown in the figure given below, the current flowing through resistance is . The value of is ________. [2023]

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Solution

Q.
In the circuit diagram shown in the figure given below, the current flowing through resistance $3 Ω$ is $\frac{x}{3} A$ . The value of $x$ is ________. [2023]

Ans.
(1)

$E = E_{2} - E_{1} = 8 - 4 = 4 V$

$\frac{1}{3} + \frac{1}{6} = \frac{1}{2} = \frac{1}{R}$

$\Rightarrow R = 2 Ω$

$The current supplied by battery E,$

$I = \frac{E}{1.5 + 4.5 + 2} = \frac{4}{8} = 0.5 A$

$Hence current in 3 Ω resistance,$

$I_{1} = (\frac{6}{3 + 6}) \times 0.5 = \frac{1}{3} A$

$\Rightarrow I_{1} = \frac{x}{3} = \frac{1}{3}$

$∴$ $x = 1$

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