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Consider two identical galvanometers and two identical resistors with resistance R. If the...

Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers Rc<R2, which of the following statement(s) about any one of the galvanometers
is(are) true ?
The maximum voltage range is obtained when all the components are connected in series
The maximum voltage range is obtained when the two resistors and one galvanometer are connected in series, and the second galvanometer is connected in parallel to the first galvanometer
The maximum current range is obtained when all the components are connected in parallel
The maximum current range is obtained when the two galvanometers are connected in series and the combination is connected in parallel with both the resistors.
Solution:

i=E2R+2Rc Vg1=iRc=ERc2(R+Rc)=ERc2R+2Rc

i2=E2R+Rc2 Vg2=i22×Rc
=12(E2R+Rc2)×Rc
Vg2=ERc4R+Rc ....(2)
Since Rc<R2  (2Rc<R)
2R+2Rc<3R
Vg1>Vg2

 


iA=ERc

Here i=E(2R+2Rc)2R.2Rc=E(R+Rc)2RRc
iB=2R2R+2Rc×E(R+Rc)2RRc=E2Rc
iA>iB