Wheatstone Bridge
WHEATSTONE'S PRINCIPLE
The most widely accepted method of measuring resistance was developed in 1843 by Charles Wheatstone, who was considered as the first Professor of Physics at Kings College, London. The Wheatstone's bridge consists of four resistors of resistances P, Q, R and S connected to form a closed network ACBD. A cell is connected between A and B. A sensitive galvanometer of resistance G is connected between C and D. The current flowing through each branch of the circuit is shown in the diagram.
Applying Kirchhoff's rule to the mesh ACDA
i1P + igG - i2R = 0 -------------- (1)
For the mesh CBDC
i3Q — i4S - igG = 0 ---------------- (2)
The resistance P, Q, R and S are so adjusted that the galvanometer current ig is zero. Then the network is said to be balanced. Then,
i1 = i3, i2 = i4and ig = O.
From equation (1),
i1P — i2R = 0 ; Therefore, i1P = i2R
From equation (2),
i1Q — i2S = 0 ; Therefore, i1Q = i2S
Dividing eqn (3) with eqn (4)
P/Q = R/S
This is Wheatstone's principle.
APPLICATIONS OF WHEATSTONE'S BRIDGE
The basic use of Wheatstone's bridge is to find the resistance of a conductor. The conductor of unknown resistance X is connected to the fourth arm of the bridge. When the bridge is balanced,
P/Q= R/X, Therefore, X =(Q/P) x R
If the values of P, Q and R are known, the resistance X of the conductor can be calculated.
Practical devices based on Wheatstone's principle are Metre Bridge, Post Office Box, Carey Fosters Bridge (modified form of Metre Bridge), Calender and Griffith Bridge etc.
The Wheatstone principle can also be used to measure
(i) Temperature (Platinum resistance thermometer)
(ii) Temperature coefficient of resistance etc.
(i) Temperature measurement
The electrical resistance of a metallic wire is found to increase gradually and fairly uniformly with temperature over a wide range, and consequently based on this property a system of thermometry has been devised.
The relation between the resistance of a metallic wire and its temperature may be represented roughly by the equation
Rt = R0(1 + αt) -------------- (1)
where R0 is the resistance of the wire at 0°C, Rtits resistance at any temperature t°C and α its temperature coefficient of resistance. Pure platinum wire, free from alloy with carbon, silicon, tin or other impurities, when not subjected to strain possesses always the same resistance at same temperature and its variation with temperature can be represented fairly by the equation
Rt = R0(1 + αt). Hence platinum wire is used for the resistance thermometer.
From equation (1)
α = (Rt – R0)/(R0 x t) ---------- (2)
The platinum resistance thermometer T is connected in the fourth arm CD of the Wheatstone's bridge. Its resistance R0 and R100 are measured by keeping it in melting ice and boiling water at standard pressure.
From equation (2)
α = (R100 – R0)/(R0 x 100) -------- (3)
Now, the resistance Rt of the thermometer is measured by keeping it in the bath whose temperature t is to be measured. Then
α = (Rt – R0)/(R0 x t) ------------ (4)
From equation (3) and (4),
(R100 – R0)/(R0 x 100) = (Rt – R0)/(R0 x t)
Therefore, i = [(Rt – R0)/(R100 – R0)] x 100
From this equation, temperature t of the bath can be calculated.
A graph can be drawn with resistance Rt along the Y-axis and known temperature t along the X-axis. The graph is a straight line with Y-intercept R0. From this calibration curve the unknown temperature x can be noted by measuring the resistance of the platinum resistance at the temperature x.
In the actual experiment a modified form of Wheatstone's bridge, the Calendar and Griffith bridge is used to determine the resistances of the platinum wire at 0°C, 100°C and t°C.
(ii) Temperature coefficient of resistance
By measuring the resistances R0 and R100of a metallic wire at 0°C and 100°C using Wheatstone's bridge, the temperature coefficient of resistance of the material of the wire can be calculated by the equation,
α = (R100 – R0)/(R0 x 100)