question_answer

For me circuit shown in figure,

A)  resistance\[R=46\Omega \]

B)  current through \[20\Omega \] resistance is\[0.1\,\,A\]

C)   potential difference across the middle resistance is\[2V\]

D)   All of the above are true

Correct Answer: D

Solution :

\[\frac{1}{R'}=\frac{1}{10}+\frac{1}{10}+\frac{1}{20}\] \[\Rightarrow \]               \[R'=\frac{20}{5}=4\Omega \] Now, using Ohm's law,\[i=\frac{25}{R+R'}\] \[\Rightarrow \]               \[0.5=\frac{25}{R+4}\] \[\Rightarrow \]               \[R+4=\frac{25}{0.5}\] \[\Rightarrow \]               \[R=50-4=46\Omega \] Current through \[20\Omega \] resistor                 \[=\frac{0.5\times 5}{20+5}=\frac{2.5}{25}=0.1\,\,A\] Potential-difference across middle resistor                 = Potential difference across\[20\Omega \]                 \[=20\times 0.1=2\,\,V\]