Post Office Box Explained Simply with Easy Examples

A post office box is a portable Wheatstone bridge packed in a wooden box with plug-type resistance coils and keys. It was originally used by post office engineers to test telegraph lines, hence the name. It measures unknown resistance from about 1 Ω to a few mega-ohms by the null balance method.

Its purpose is practical: instead of building a bridge with loose wires each time, you get ready ratio arms and a variable known arm in one box, a battery key and a galvanometer key. That makes quick and repeatable resistance measurements possible in the field and in school labs.

Key Concepts

Ratio arms P and Q: fixed resistors selected by plugs, values 10 Ω, 100 Ω and 1000 Ω. Known arm R: adjustable resistance from 1 Ω to 5000 Ω or more, set by removing plugs. Unknown arm X: resistor connected between two terminals. Balance condition: P/Q = R/X. Null point: galvanometer shows no kick when both keys are pressed in the right order. Always close the battery key before the galvanometer key to avoid inductive kicks.

How It Works

1. Connect the unknown resistor across the X terminals and the galvanometer and battery to their marked terminals.
2. Choose ratio arms, usually P = Q = 100 Ω for a first trial, so X ≈ R.
3. Remove plugs in the R arm, starting from large values downward, and tap the galvanometer key to see which side the needle kicks.
4. Adjust R by 1 Ω steps until pressing the key gives no deflection. That R satisfies the balance condition.
5. Calculate X = R × Q/P. Repeat with ratios 10:1000, 100:100 and 1000:10 to get more significant figures and average the consistent value.

Removing a plug inserts that coil in series; pressing a plug firmly keeps contact resistance negligible. Missing plugs or dirty contacts are the usual source of error.

Worked Example

With ratio arms P = 100 Ω and Q = 100 Ω, balance is obtained at R = 47 Ω.

1. Balance formula X = R × Q/P.
2. X = 47 × 100/100 = 47 Ω.
3. Check with P = 1000 Ω, Q = 100 Ω: now R should be 470 Ω for the same X.

The unknown resistance is 47 Ω, confirmed by two different ratios, which improves confidence and significant figures.

Common Misconceptions

• Removing a plug disconnects that resistor: In this box removing a plug actually includes that coil in the circuit; a pressed plug short-circuits it out.
• One balance is always enough: Using several ratios reveals contact errors and gives extra digits of accuracy.
• Key order does not matter: Pressing the galvanometer before the battery can cause large induced deflections and false readings.

Real-World Applications

• Historical telegraph and telephone line testing and fault detection.
• School laboratory measurement of unknown resistors and wire resistivity.
• Quick checking of coils, heating elements and winding resistances.

The post office box packages the Wheatstone bridge into a rugged, plug-selectable instrument that trades length measurement for clean ratio arithmetic to find any unknown resistance.