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.)

Dear student

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

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