The Wheatstone Bridge, Meter Bridge and Potentiometer

The wheatstone bridge is one of the most accurate methods of measuring resistance. It consists of four resistors of resistance R₁, R₂, R₃ and R₄ connected as shown below.

When no current flows through the galvanometer, the bridge is said to be balanced.

Therefore, p.d across R₁ = p.d across R₃

And  p.d across R₂ = p.d across R₄ 

Hence, I1R1=I2R3 ——–(1) and

I1R2=I2R4 ——–(2)

Dividing (1) by (2), we have,

R1R2=R3R4

Where R₁ is the unknown resistance, R₂ is a fixed resistance of known value, R₃ & R₄ are variable resistances of known values.

Wheatstone Bridge Slide show. Click slides:

The Metre Bridge

It consists of a straight uniform resistance wire AB of length 1m stretched along a metre rule. The  unknown resistor X is placed at the left side, while the known R is placed at the right side.

When the circuit is closed, a point is located along the resistance wire with the jockey when G reads zero.

At this point, X ∞ l₁ and R ∞ l₂

∴ X = kl₁ and R = kl₂

Since k is the same,

∴XI1=RI2∴X=RI1I2

Precautions:

1. The value of the known resistance Rshould be chosen so that the balance point comes between 30cm and 70cm.
2. The battery key should always be depressed before the Gcontact is made on the bridge wire.
3. Avery small current should be passed through the galvanometer to avoid damage.
4. In other not to destroyed the uniformity of the wire, the jockey should touch the wire

The Potentiometer

A potentiometer consists of uniform resistance wire AB of length 100cm through which a source of emf maintains a steady current.

Since the wire is uniform and current constant,

V∝R∝IV=kL

When a potentiometer is used to compare the emfs of two cells, at balance point when G reads  zero,

E1E2=I1I2

Merits of the Potentiometer Over the Voltmeter

1. The potentiometer is a more accurate in measuring voltage than the voltmeter.
2. There is no zero scale error as that associated with pointer instrument like voltmeter.
3. It passes no current at the time current is being taken.