question_answer

What is the current flowing in arm AB?

A)  \[\frac{35}{4}A\]

B)  \[\frac{13}{7}A\]

C)  \[\frac{5}{7}A\]

D)  \[\frac{7}{5}A\]

Correct Answer: B

Solution :

 Key Idea : As per Kirchhoff s law \[\sum{iR}=V\] Let \[{{i}_{1}},{{i}_{2}}\]be current in the two loops of the given circuit then Applying Kirchhoff s law to loop 1, we get \[(\sum{iR=V})\] \[8{{i}_{1}}+2({{i}_{1}}+{{i}_{2}})=10\] \[\Rightarrow \] \[10{{i}_{1}}+2{{i}_{2}}=10\] \[\Rightarrow \] \[5{{i}_{1}}+{{i}_{2}}=5\] ?(i) Applying kirchhoffs law to loop 2, we get \[4{{i}_{2}}+2({{i}_{1}}+{{i}_{2}})=8\] \[\Rightarrow \] \[6{{i}_{2}}+2{{i}_{1}}=8\] \[\Rightarrow \] \[{{i}_{1}}+3{{i}_{2}}=4\] ?(ii) From Eqs. (i) and (ii), we get \[{{i}_{1}}=\frac{11}{14}A,{{i}_{2}}=\frac{15}{14}A\] Hence current flowing is arm AB is \[{{i}_{1}}+{{i}_{2}}=\frac{11}{14}+\frac{15}{14}=\frac{26}{14}=\frac{13}{7}A\]