Wheatstone Bridge

For measuring accurately any electrical resistance Wheatstone bridge is widely used. There are two known resistors, one variable resistor and one unknownresistor connected in bridge form as shown below. By adjusting the variableresistor the current through the Galvanometer is made zero. When thecurrent through the galvanometer becomes zero, the ratio of two knownresistors is exactly equal to the ratio of adjusted value of variable resistanceand the value of unknown resistance. In this way the value of unknown electrical resistance can easily be measured by using a Wheatstone Bridge.

Wheatstone Bridge Theory

The general arrangement ofWheatstone bridge circuit is shown in the figure below. It is a four arms bridge circuit where arm AB, BC, CD and AD are consisting of electrical resistances P, Q, S and R respectively. Among these resistances P and Q are known fixedelectrical resistances and these two arms are referred as ratio arms. An accurate and sensitive Galvanometer is connected between the terminals B and D through a switch S2. The voltage source of this Wheatstone bridge is connected to the terminals A and C via a switch S1 as shown. A variable resistor S is connected between point C and D. The potential at point D can be varied by adjusting the value of variableresistor. Supposecurrent I1 and current I2are flowing through the paths ABC and ADC respectively. If we vary the electrical resistancevalue of arm CD the value of current I2 will also be varied as thevoltage across A and C is fixed. If we continue to adjust the variable resistance one situation may comes when voltage drop across the resistor S that is I2.S is becomes exactly equal tovoltage drop across resistor Q that is I1.Q. Thus the potential at point B becomes equal to the potential at point D hence potential difference between these two points is zero hencecurrent through galvanometer is nil. Then the deflection in the galvanometer is nil when the switch S2 is closed.

Now, from Wheatstone bridge circuit

and

Now potential of point B in respect of point C is nothing but the voltage drop across theresistor Q and this is

Again potential of point D in respect of point C is nothing but the voltage drop across theresistor S and this is

Equating, equations (i) and (ii) we get,

Here in the above equation, the value of S and P ⁄ Q are known, so value of R can easily be determined.

The electrical resistances P and Q of the Wheatstone bridge are made of definite ratio such as 1:1; 10:1 or 100:1 known as ratio arms and S the rheostat arm is made continuously variable from 1 to 1,000 Ω or from 1 to 10,000 Ω