question_answer

            [a]   In the given circuit the internal resistance of the 18 V cell is negligible. If \[{{R}_{1}}\,\,=\,\,400\,\Omega \],  \[{{R}_{3}}=100\text{ }\Omega \] and \[{{R}_{4}}=500\Omega \]and the reading of an ideal voltmeter across \[{{R}_{4}}\] is 5 V, then the value of \[{{R}_{2}}\] will be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) \[550\text{ }\Omega \]                           

B) \[450\text{ }\Omega \]

C) \[230\,\,\Omega \]          

D)               \[300\,\,\Omega \]

Correct Answer: D

Solution :

\[{{V}_{{{R}_{4}}}}^{~}=~5\,Volt\] \[\,I{{R}_{4}}^{~}=~5\,\] or  \[I=\frac{5}{500}\,\,=\,\,\frac{1}{100}\,Amp.\] \[\Rightarrow \,\,{{V}_{{{R}_{2}}}}=\frac{1}{100}(100+500)=6\,volt.\] So, V across \[400\text{ }\Omega \] will be \[18-6=12\] volt \[\Rightarrow \]Total current\[=\,\,\frac{12}{400}\,Amp.\] \[\Rightarrow \]I across \[{{R}_{2}}=\frac{12}{400}-\frac{1}{100}=\frac{8}{400}\] Amp. Now\[\frac{8}{400}{{R}_{2}}=6\] So, \[{{R}_{2}}=300\text{ }\Omega .\]