In the following network, the current through galvanometer will

Consider the following diagram:

As the bridge is not balanced so the current will flow through wire.
Consider the loop PSQP:
\(
-(I-i)-i_g G+4 i=0
\)
\(\Rightarrow-I-i_g G+5 i=0 \quad---(1)\)
Now, consider the loop SQRS:
\(
\begin{aligned}
& -i_g G-4\left(i+i_g\right)+3\left(I-i-i_g\right)=0 \\
& \Rightarrow+3 I-i_g(G+7)-7 i=0 \quad--(2)
\end{aligned}
\)
On considering following operation, \(7 \times \mathrm{eq}^{\mathrm{n}}(1)+5 \times \mathrm{eq}^{\mathrm{n}}(2)\)
\(\begin{aligned} & 4 I-i_g(12 G-35)=0 \\ & \Rightarrow i_g=\frac{4 I}{(12 G+35)}\end{aligned}\)
Therefore, the current will flow through from \(\mathrm{S}\) to \(\mathrm{Q}\), as the value of \(I\) and hence, the value of \(i_g\) will be positive. As, \(\mathrm{G}\) is also positive, it is the resistance of the galvanometer.