
If a large resistance R is connected with a battery, then current will be approximately Rϵ, and t will remain almost constant.
In 1st case, only (G) is connected ⇒ig=i
In 2nd case,
igR0=(I−ig)S⇒(ig)2=(Rg+SS)i
If (ig)2=31(ig),⇒(Rg+SS)i=31i
Rg=2S