Purpose: You will learn the theory and construction of a Wheatstone Bridge and use it to measure ohmic resistors accurately.
References: Giancoli, p. 619 ; Serway, p. 782.
Supplies: Bring note paper, calculator, graph paper, and a straight edge.
Theory: As you discovered in the Electrical Resistance experiment you have trouble trying to read a volt meter or ammeter to better than a few percent accuracy, and this produces a corresponding uncertainty in your value for R. The Wheatstone Bridge (Fig.1) is a circuit which compares the unknown resistance RX to a standard resistor RS and to two calibrated variable resistors R1and R2, all whose values are known with high precision (in our experiment 1%).
Furthermore, the galvanometer is used as "null detector" (as it was in the Equipotential Plotting experiment) so all you look for is a movement of the needle and not an absolute meter reading.
Although it is possible to derive a general equation for the resistances, currents, voltage supplies, etc., we are interested only in the case
VCD=VCB.................(1)
i.e.. no potential differences between points B and D. This means there will be no current through the galvanometer so
Ix=I1 and Is=I2..............(2)
We can write VCD = I1R1 and VCB = I2R2 and use (1) to obtain
I1R1 = I2R2....................(3)
Now VCA = VCD + VDA = VCB + VBA so again using (1) we have
VDA = VBA.................(4)
Writing VDA = IxRx and VBA = IsRs and using (4) gives
I1Rx = I2Rs............(5)
We now divide (5) by (3) to get
or,
......(6)
This is the balance equation for the Wheatstone Bridge. In using this equation you must have the resistors labeled as in Fig. 1; if you change the labeling you must change the subscripts in (6) accordingly.
Now if you look at the balance equation you notice that it does not involve either the current through RX or the voltage applied to the bridge. This is quite desirable when measuring ohmic resistances since variations in the power supply voltage do not effect the balance conditions. The other side of the coin is that the bridge is not useful in measuring non-ohmic resistances since in that case R depends on I which is undetermined.
Finally, if an A.C. voltage supply and some form of A.C. meter are used then the bridge may be converted to measuring either capacitance or inductance. Instead of using V= IR for the voltage drops the expressions become V = Q/C and V = L di/dt, respectively.