question_answer

In the circuit shown, the current through the\[5\,\Omega \]resistor is

A)  \[\frac{8}{3}A\]                               

B)         \[\frac{9}{13}A\]

C)  \[\frac{4}{13}A\]            

D)         \[\frac{1}{3}A\]

E)  \[\frac{2}{3}A\]

Correct Answer: D

Solution :

                \[\frac{1}{R}=\frac{1}{2}+\frac{1}{2}=1\]                 \[R=1\,\Omega \] Total resistance\[=R+5=1+5=6\,\Omega \]                 \[{{E}_{eff}}=\frac{{{E}_{1}}{{r}_{1}}+{{E}_{2}}{{r}_{2}}}{{{r}_{1}}+{{r}_{2}}}=\frac{2\times 2+2\times 2}{2+2}\]                                 \[=2\,V\]                 \[i=\frac{{{E}_{ff}}}{R}=\frac{2}{6}=\frac{1}{3}A\]