3.9.3 Experimental principles
1)The basic principle of the Wheatstone bridge
As a basic and important instrument in electromagnetics,electrical bridge is mainly used for measuring the resistance of resistor,inductance of the coil,the capacitance of capacitor and its loss as well.Bridges with different functions have been developed,such as DC bridges and AC bridges,for different purposes.Among them,a single arm electric bridge(also called Wheatstone bridge)is the simplest one,which is suitable for measuring median resistance in the range of 1～1 000 000 Ω.
The basic circuit of Wheatstone bridge is shown in Figure 3.9.1.It mainly consists of four bridge arms,the bridge balance indicator(galvanometer),power supply,switch and other components.When the electric potential at position C is equal to that at position D,there is no current flowing in the galvanometer(Ig=0).At this moment,the bridge is in the status of balance,which can be expressed as:
According to Equations(3.9.1)and Equation(3.9.2),it can be further derived:
Figure 3.9.1 Principle of Wheatstone bridge circuit
If R0,R1 and R2(or R1/R2)are known,then the unknown Rx can be calculated by the following equation:
The equation above is called the bridge balance condition.Thus,the unknown resistance Rx can be calculated by the multiplication of the ratio between R1 and R2 and the standard resistance R0.
In order to eliminate the systematic error caused by the possible inaccuracy of R1 and R2,we can further exchange the positions of Rx and R0 while maintaining the ratio R1/R2 under the same conditions.By readjusting the standard resistance R0,a new balance can be reached again.If the new standard resistance value is R′0,then the formula of bridge balance condition can be described as follows:
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According to Equations(3.9.4)and Equation(3.9.5),it can be derived as:
The equation above shows that exchange measurements can eliminate the error introduced by R1 and R2.
2)The sensitivity of the Wheatstone bridge
In the experiment,the equilibrium state is determined by the current of galvanometer in the bridge.It depends on the deflection of the pointer from equilibrium position in the galvanometer.When the flowing current is very small,the deflection is also too slight to be observed,leading to the limited sensitivity.Therefore,the sensitivity of the Wheatstone bridge is introduced and defined as follows:
WhereΔRx is a very small change of Rx after the equilibrium state(change R0 in reality),Δn is the number of deflection grids of the galvanometer pointer.In practice,the sensitivity of Wheatstone bridge is defined as another equation:
The sensitivity of the Wheatstone bridge can be improved by the following methods:
(1)Increase the voltage of the DC power supply appropriately when the rated power of bridge arm resistances is not exceeded.
(2)Select a galvanometer with higher sensitivity and lower resistance.
(3)Reduce the resistance of R0 appropriately according to the actual situation if possible.
(4)Select proper ratio of R1/R2.The sensitivity is the highest when the value of the ratio R1/R2 is 1.
