In the given network,the current through bran | vedclass

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(D) Let the potential at the common upper node $ABCD$ be $V_1$ and the potential at the common lower node $HGFE$ be $V_2$. Let $V_1 - V_2 = V$.
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Vedclass · Accepted Answer

$-0.258$

Vedclass · Answer

(D) Let the potential at the common upper node $ABCD$ be $V_1$ and the potential at the common lower node $HGFE$ be $V_2$. Let $V_1 - V_2 = V$.
Using Millman's theorem,the equivalent voltage $V$ across the parallel branches is given by:
$V = \frac{\sum \frac{E_i}{r_i}}{\sum \frac{1}{r_i}} = \frac{\frac{10}{2} + \frac{15}{2} + \frac{20}{4} + \frac{25}{5}}{\frac{1}{2} + \frac{1}{2} + \frac{1}{4} + \frac{1}{5}} = \frac{5 + 7.5 + 5 + 5}{0.5 + 0.5 + 0.25 + 0.2} = \frac{22.5}{1.45} = \frac{2250}{145} = \frac{450}{29} \, V$.
The current $I_{BG}$ through branch $BG$ (containing $15 \, V$ and $2 \, \Omega$) is given by:
$I_{BG} = \frac{E_2 - V}{r_2} = \frac{15 - \frac{450}{29}}{2} = \frac{\frac{435 - 450}{29}}{2} = \frac{-15}{58} \approx -0.258 \, A$.
Since the question asks for the current magnitude and the provided options are not matching the calculation,we re-evaluate the circuit. If we assume the question asks for the current in a different configuration or there is a typo in the options,based on standard nodal analysis,the current is small. Given the options,none are correct. However,if we assume the question implies a different circuit or is flawed,we must note that the current is approximately $0.26 \, A$. Given the options,$0$ is the closest value.

In the given network,the current through branch $BG$ is almost equal to ............ $A$.

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