question_answer

In this circuit, the value of \[{{I}_{2}}\] is

A)  \[0.2\text{ }A\] 

B)  \[0.3\text{ }A\]

C)  \[0.4\text{ }A\]

D)  \[0.6\text{ }A\]

Correct Answer: C

Solution :

:             From figure, Voltage across all the three branches is the same. \[\therefore \] \[10{{I}_{1}}=15{{I}_{2}}=30{{I}_{3}}\] or \[{{I}_{1}}=1.5{{I}_{2}}\]                           ?....(i) \[15{{I}_{2}}=30{{I}_{3}}\] or \[{{I}_{3}}=\frac{1}{2}{{I}_{2}}\] ???..(ii) Also \[I={{I}_{1}}+{{I}_{2}}+{{I}_{3}}\] \[1.2=1.5{{I}_{2}}+{{I}_{2}}+\frac{1}{2}{{I}_{2}}\](Using (i) and (ii)) \[=\frac{3{{I}_{2}}+2{{I}_{2}}+{{I}_{2}}}{2}\]