Wheatstone Bridge Background

A current flows in an electrical circuit driven by the potential difference at the battery. Resistance, current and voltage are connected by Ohm's law
U=RI
where U is the voltage, R the resistance and I the current.

The current and potential difference (= measured voltage) in each part of the circuit can be calculated with the help of Kirchhoff's rules

  1. The sum of the potential drops around any circuit loop must equal the sum of the potential increases
  2. At a junction point in a circuit where the current can divide, the sum of the currents into the junction must equal the sum of the currents out of the junction.
Look at the following setup:

The potential drop across the multimeter is zero if
I1*R1=I3*Rx and
I2*R2=I4*R4
and as the potential drop over the galvanometer is zero, so is the current and we have
I1=I2 and
I3=I4
With this equation we see that the unknown resistance is given by
Rx=(R1/R2)*R4

Multimeter

The current and the potential drop are measured via a current flowing through a galvanometer. A galvanometer is a small coil suspended in a magnet. A change in current puts the coil in a new position. However, only a very small current can flow through this galvanometer moves the coil. Voltage is measured by putting the galvanometer across the voltage drop to be measured. Current is measured by putting the multimeter in the circuit itself. Thus, a voltmeter needs a high resistance to make the most accurate measurement and a ammeter a very low resistance. At the same time the current over the galvanometer has to be kept very small. Here is how the circuit inside a voltmeter and an ammeter looks: