The equivalent resistance between the points A and B in the following circuit is x 5 ? . The value of x is __________. [2026]

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Solution

Q.
The equivalent resistance between the points A and B in the following circuit is $\frac{x}{5} Ω$ . The value of $x$ is __________. [2026]

Ans.
(21)

$6 i_{1} + 3 (2 i_{1} - i) = 3 (i - i_{1})$

$\Rightarrow 15 i_{1} = 6 i \Rightarrow i_{1} = \frac{2}{5} i . . . (1)$

$3 (i - i_{1}) + 6 i_{1} = 1$

$3 i + 3 i_{1} = 1$

$(3 + \frac{6}{5}) i = 1$

$\Rightarrow i = \frac{5}{21} A = \frac{1 V}{R_{eq}} \Rightarrow R_{eq} = \frac{21}{5} Ω$

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