In the figure shown PQ is a potentiometer wire. When galvanometer is connected at A, it shows zero deflection when PJ = x. Now the galvanometer is connected to B and it shows zero deflection when PJ = 3x. Find the value of unknown resistance Rₓ in term of R.

Question

G1 Physics · Accepted Answer

Image Balance length is proportional to potential difference. Thus V(P,A)/V(P,B) = x/(3x)=1/3. In the lower divider, V(P,A) = IR and V(P,B) = I(R+Rₓ). Therefore R/(R+Rₓ)=1/3, giving Rₓ=2R.