In a bridge circuit shown in Figure $1$ below, strain gage represents R$1.$ The strain$-$gage resistance strain is $140.R2=R3=120.$ The galvanometer resistance is $75.$

$[6$ Marks$]$

$($a$)$ Find the value of $R4$ to bring the bridge into balance at zero$-$strain conditions.

$($b$)$ Calculate the galvanometer current when $=450\frac{m}{m}.$

$($Gage factor is $2\mathrm{.}0$ and the battery voltage is $5\mathrm{.}0$ V $.)$