Determine the current flowing through the galvanometer (G) as shown in the figure.

Explanation

Current flowing through the circuit, `I=2A`
Applying Kirchoff.s law at junction P, `I=I_(1)+I_(2)`
`I_(2)=I-I_(1)" "…(1)`
Applying Kirchoff.s `II^(nd)` law at junction PQSP
`5I_(1)+10I_(g)-15I_(2)=0`
`5I_(1)+10I_(g)-15(I-I_(1))=0`
`5I_(1)+10I_(g)-15I+15I_(1)=0`
`20I_(1)+10I_(g)=15I`
`20I_(1)+10I_(g)=15xx2`
`divide` by `10 rArr 2I_(1)+I_(g)=3 " " ...(2)`
Applying Kirchoff.s `II^(nd)` law at junction QRSQ
`10(I_(1)-I_(g))-20(I-I_(1)+I_(g))-10I_(g)=0`
`10I_(1)-10I_(g)-20(I-I_(1)+I_(g))-10I_(g)=0`
`10I_(1)-10I_(g)-20I+20I_(1)-20I_(g)-10I_(g)=0`
`30I_(1)-40I_(g)=20I`
`divide` by `10rArr 3I_(1)-4I_(g)=2I`
`3I_(1)-4I_(g)=2xx2=4`
`{:("equ" (2) xx 3" "6I_(1)+3I_(g)=9),("equ"(3) xx 2" " 6I_(1)-8I_(g)=8),(" "ul((-)" " (+)=(-))),(" "ul(11I_(g)=1)):}`
`I_(g)=(1)/(11)A`