d
Applying kirchoff's loop law in \(A B P_{2} P_{1} A\) we get

\(-2 i+5-10 i_{1}=0\)         .......\((i)\)

Again applying kirchoff's loop law in \(P_{2} C D P_{1} P_{2}\) we get,

\(10 i_{1}+2-i+i_{1}=0\)        .....\((ii)\)

From \((i)\) and \((ii)\)  \(11 i_{1}+2-\left[\frac{5-10 i_{1}}{2}\right]=0 \)

\({\Rightarrow i_{1}=\frac{1}{32} \text { A from } P_{2} \text { to } P_{1}}\)