b
Current through arm \(C A D\),   \(I=\frac{V}{8}\, amp\)

Potential difference between \(C\) and \(A=V_{C}-V_{A}\)

\(=\frac{V}{8} \times 4=\frac{V}{2}\, \mathrm{volt}\)

Current through \(C B D\),   \(I^{\prime}=\frac{V}{4}\, amp\)

Potential difference between \(C\) and \(B=V_{C}-V_{B}\)

\(=\frac{V}{4} \times 1=\frac{V}{4} \,\text { volt. }\)

Potential between \(A\) and \(B=V_{A}-V_{B}\)

\(\therefore \quad V_{A}-V_{B}=V_{C}-V_{B}-\left(V_{C}-V_{A}\right)=\frac{V}{4}-\frac{V}{2}=\frac{V}{4}\)

\( \Rightarrow {V_A} - {V_B} < 0\quad or,\quad {V_A} < {V_B}\)

As \({V_A} < {V_B}\), so direction of current will be from \(B\) to \(A\).