The physics
A Wheatstone bridge has four arms. A galvanometer joins the middles of its two branches. The bridge balances when no current crosses the middle.
P / Q = R / S
A metre bridge uses a 100 cm uniform wire for two of the arms. The jockey splits it into l and 100 − l. At the null point the needle rests.
X / R = l / (100 − l)
Only the ratio of the two lengths matters. The wire's thickness and its total resistance do not.