Download 104-lab4-Wheatstone

Physics 184
Experiment 4
WHEATSTONE BRIDGE, SERIES AND PARALLEL
RESISTANCES
Object:
To learn how to operate a Wheatstone Bridge and to verify the formulas for the combination of
resistances.
Apparatus:
Slide wire Wheatstone Bridge, resistance box, unknown resistors, galvanometer and a battery or
power supply.
Theory:
A Wheatstone Bridge is 4 resistors connected in the form of a square with galvanometer connected
across one diagonal and a voltage source across the other, as shown in the circuit below. When the
galvanometer indicates zero current, the bridge is balanced. In this condition, the current, I, branches
at A with one part, IB, passing through point B and the remainder, IC, passing through point C. The
two parts recombine at point D. Since no current flows through the the galvanometer, G, at this
condition, the voltage drop from A to B must be the same as that from A to C. Similarly, the voltage
drop from B to D must be the same as that from C to D. Thus:
IBR1 = ICR4
Dividing one equation by the other:
and
R1 /R2 = R4 /R3
Figure 1. Wheatstone Bridge
IBR2 = ICR3
or R1 R3 = R4 R2
In practice, only one resistance is unknown and the others are known and variable. In the slide wire
Wheatstone Bridge, two of the resistances are the two ends of the wire divided by the sliding
contact. In the diagram, the slide wire is represented by R4 and R3. and the sliding contact is the
point C. Since the resistance per unit length of the slide wire is constant, the lengths of the two ends
of the slide wire, L4 and L3, may be substituted for R4 and R3, respectively. If, also, an unknown
resistor, xn, is inserted in place of R1, and a standard resistor, RS, inserted in place of R2, the above
expression may be written:
xn = RS (L4 / L3).
Figure 2. Bridge For Determining Unknown Resistance
Procedure and Data Analysis (the report can be finished and turned in during the lab session):
1. Connect the circuit like in Fig 3, with a resistance (may be 10 or 20 Ohms) on the resistance box
at all times.
2. Place one of the unknown resistances, xn, in the circuit and set a resistance in the resistance box
RS . Adjust RS until the position of the sliding contact is between 0.6 and 0.6 m, when the
galvanometer indicates zero current. Record your data for the lengths and RS , and calculate value
of xn.
3. Repeat step 2 with the other unknown resistances.
4. Measure the resistance of all the unknown resistances in series. When resistances are connected in
series, the equivalent resistance is just the sum of the individual resistances. Find the percent
difference between the measured value of these resistances in series and the value calculated from
the measurement of the resistances, individually.
5. Measure the resistance of the unknown resistances in parallel. When connected in parallel, the
reciprocal equivalent resistance is equal to the sum of the reciprocals of the individual resistances.
Find the percent difference between the measured and calculated values of the resistances in
parallel.
Figure 3. Physical Layout Of Circuit