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In the circuit, $E_1=E_2=E_3=2 V$ and $R_1$ and $\mathrm{R}_2=4 \mathrm{~W}$. Then the current flowing through $\mathrm{E}_2$ is
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The correct answer is:
$2 \mathrm{~A}$ from $\mathrm{B}$ to $\mathrm{A}$
$$
\begin{aligned}
& E_{e q}=\frac{\frac{E_1}{R_1}+\frac{E_3}{R_2}}{\frac{1}{R_1}+\frac{1}{R_2}}=\frac{E_1 R_2+E_3 R_1}{R_1+R_2}=\frac{2 \times 4+2 \times 4}{42+4}=2 V \\
& R_{e q}=\frac{R_1 R_2}{R_1+R_2}=\frac{4 \times 4}{4 \times 4}=2 \Omega \\
& -E_2+i R_{e q}-E_{e q}=0 \\
& i=\frac{E_2+E_{e q}}{R_{e q}}=\frac{2+2}{2}=2 A
\end{aligned}
$$
Hence, the current flowing through $\mathrm{E}_2$ is $2 \mathrm{~A}$ from $\mathrm{A}$ to $\mathrm{B}$
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