question_answer

An ideal ammeter (zero resistance) and an ideal voltmeter (infinite resistance) are connected as shown. The ammeter and voltmeter reading for \[{{R}_{1}}=5\Omega ,\,{{R}_{2}}=15\,\Omega ,{{R}_{3}}=1.25\Omega \]and \[E=20V\] are given as

A)  \[6.25A,\,\,3.75V\]        

B)  \[3.00A,\,5V\]

C)  \[3.75A,\,3.75V\]        

D)  \[6.25A,6.25V\]

Correct Answer: B

Solution :

\[{{R}_{eq}}={{R}_{1}}+{{R}_{2}}\] (Series combination) \[{{R}_{eq}}\]of the circuit \[=\frac{5\times 15}{5+15}+\frac{125}{100}=\frac{75}{20}+\frac{5}{4}5\Omega \] We know that \[I=\frac{E}{{{R}_{eq}}}=\frac{20}{5}=4A\] Potential difference across \[{{R}_{1}}\]and \[{{R}_{2}}\] are same (Parallel combination) \[{{I}_{1}}{{R}_{1}}=(4-{{I}_{1}}){{R}_{2}}\] \[\Rightarrow \]\[5{{I}_{1}}=(4-{{I}_{1}})\times 15\Rightarrow {{I}_{1}}=12-3{{I}_{1}}\Rightarrow {{I}_{1}}=3A\] Thus reading of ammeter = 3A Voltage across \[1.25\Omega =I\times R=4\times 1.25=5V\] (Reading of voltmeter)