Metre bridge: find the unknown resistance.

A metre bridge: drag the jockey along a 100 cm wire until the galvanometer reads zero and get the unknown from R·l/(100 − l)

Find the balance point for a hidden resistor and read its value to ±0.2 Ω, then choose R so balance falls between 40 and 60 cm.

Ignoring that the bridge is most sensitive with balance near the middle.

• Four resistors form a closed loop; a battery is connected across one pair of opposite corners and a galvanometer across the other pair.
• The bridge is balanced when no current flows through the galvanometer; the two ends of the galvanometer are then at the same potential.
• Balance condition, using our own labels: the battery is across corners A and C; path A→B→C has P (from A to B) then Q (B to C), and path A→D→C has R (A to D) then S (D to C); the galvanometer joins B and D. The bridge is balanced when P/Q = R/S, which is the same as PS = QR (products of opposite arms equal).
• Whatever letters a figure uses, check the condition this way: take the two resistors meeting at one battery corner; each one's ratio to the resistor that follows it on its own path must be the same for both paths.
• At balance, the galvanometer branch (or any resistor put in its place) can be removed, and the network reduces to two parallel series-pairs.
• The balance condition does not depend on the emf of the battery or the resistance of the galvanometer.
• If the ratios are not equal, the bridge is unbalanced and the middle resistor carries current; then Kirchhoff's rules must be used.
• The bridge lets an unknown resistance be found from three known ones by adjusting one of them until the galvanometer shows no deflection.

Teaching this idea? Put the simulation on your own page or LMS with this code.