In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be ____? (Kindly explain how to solve this in detail.)

Question

In the circuit, the galvanometer G shows zero deflection If the
batteries A and B have negligible internal resistance, the value of
the resistor R will be ____? (Kindly explain how to solve this in
detail )

Roop Narayan · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_5880625dbcc20%20png"
style="width: 283px; height: 124px;">
assume that the currents are flowing the meshes as shown
through R, i1-i2 currents will be flowing

writing kirchoffs law-12+R(i1-i2)+500i1=0-12+Ri1-Ri2+500i1=0----(1)+2+R(i2-i1)=02+Ri2-Ri1=0Ri1-Ri2=2----(2)from 1 and 2-12+2+500i1=0-10=-500i1i1=150i2=0 (Given)from 2Ri1-Ri2=2R150=2R=100 ohmsRegards