Download Physics Laboratory

Name_____________________________________ Date_________ Partner(s)____________________________
____________________________
Physics Laboratory
Electrical Circuits - Bridge Circuits
I.
Bridge Circuits
A bridge circuit can be used to make accurate determinations of the values of unknown circuit
elements. When the unknown circuit elements are resistances, the bridge is called a Wheatstone
bridge.
R2
R1
A.
D
A circuit is set up with four resistors and a battery, as shown.
How is the current passing through R1 related to the current
passing through R2?
R3
R4
A
B
C
B.
How is the current passing through R3 related to the current
passing through R4?
C.
Can you tell whether the current through the R1 and R2 combination is larger or smaller than the
current through the R3 and R4 combination? What information is needed in order to tell which
current is greater?
R1
I1
D.
A resistor R is connected between points C and D to create a
bridge circuit. In general, current will flow through the resistor
R. However, if the voltages at points C and D are properly
adjusted, then no current flows through R. How then must the
voltages at points C and D be related? Explain.
R2
D
I2
R
I3
A
R3
R4
C
When no current flows through resistor R, then how must the currents I1 and I2 be related? How
about currents I3 and I4?
I4
B
When no current flows through resistor R, how are the voltages VAC and VAD related to each other,
and how are the voltages VCB and VDB related to each other?
Write each of the voltages VAC , VAD , VCB , and VDB in terms of current I and resistance R., for
example, VAD = I1R1.
E.
When the conditions described in part D exist in the bridge circuit, then a simple equation can be
derived that relates the resistances R1, R2, R3, and R4. In the Wheatstone bridge, three of the
resistances are known and the fourth is to be determined. For example, suppose resistances R1, R3,
R 
and R4 are known, and R2 is unknown. Then, R2 will be given by the equation R 2  R 1  4  
 R3 
Show how this equation for R2 can be derived from the equations in the above section.
In the experiment, R 2 is the unknown resistance. It will be a coil of wire made from a material
whose resistivity,  we want to determine. The equation for the resistivity of the material from
AR 2
which the coil is made is  
, where A is the cross-sectional area of the wire and L is the length
L
of the wire.
II.
Bridge Construction – the elements
A.
Examine the DC power supply. Look at the face of the power supply. Notice how to turn it on and
how to adjust the voltage and current it supplies. The power supply acts like a battery except that
chemical reactions do not produce the potential difference. Any questions? Talk with your
instructor!
B.
Examine the decade resistance box. Make sure you know how to set and read values of resistance.
C.
Examine the multimeter. Notice that it can measure a lot of different electrical quantities. Do you
know where the dial should be set when measuring different ranges of DC voltage? AC voltage?
DC current? AC current? Resistance? Capacitance? Do you know where the probes must be
connected in order to make the above measurements?
2
D.
Examine the potentiometer. A top view of the potentiometer is
shown. Notice that there are three binding posts (places where
wires can be connected to the potentiometer) and a knob that
changes the potentiometer reading. Make sure that you know how
to read the dial on the potentiometer. (The dial values go from 0.00
to 10.00.) This is important! If you’re not sure, then ask the
instructor.
Set up your multimeter to measure resistance. Connect the probes
of the multimeter to binding posts A and B on the potentiometer.
In the table below, record the value of resistance for the various dal
settings.
Potentiometer
Reading (PR)
Resistance from A to B
(ohms)
A
B
C
window
knob
Resistance from A to C
(ohms)
Resistance from C to B
(ohms)
0.00
3.00
5.00
8.00
10.00
Arbitrary (PR)
Setting
Notice for the Wheatstone bridge circuit on the first page of this lab handout, the resistances R3 and
R4 in the bridge circuit are the resistances from A to C (RAC) and from C to B (RCB) on the
potentiometer. And, in order to find the unknown resistance in the bridge we need to know the
resistance value R1 (resistance of the decade resistance box) and the ratio of resistances R4/R3, or
(resistance from C to B)/(resistance from A to C).
From section I-E above, the unknown resistance in the bridge circuit R2 is
R
R2  R1  4
 R3

resistance from C toB 
  (resistance of decade box) 
 .

 resistance from A to C 

From the above table, notice how the potentiometer readings are related to the resistances from C to
B and from A to C, and come up with a expression for the ratio of resistances in terms of the
potentiometer reading (PR). That is,
 R4

R
 3
  resistance from C to B 

  resistance frm A to C  =

3
Draw a diagram of what you think the inside of the potentiometer looks like (think voltage divider).
R1 = decade
resistance box
III. The Experiment
Construct the bridge circuit shown. Your instructor will tell
you which unknown resistance values will be determined in
this experiment. Use only seven leads (wires with banana
plugs) to make the needed connections. Notice that R1 is the
resistance of the decade resistance box, and R2 is the resistance
of the unknown resistor. R3 and R4 are the resistances
associated with the two sides of the potentiometer (A to C and
C to B). Connect the multimeter to read the voltage between
points C and D.
A.
D
R2 = unknown
resistance
R
R3 = A to C on
potentiometer
R4 = C to B on
C potentiometer
A
B
R =multimeter
DC power
supply
Procedure:
1.
Adjust the output of the DC power supply until the voltage reading on the DC power supply
meter indicates approximately 1 volt.
2.
Set the potentiometer dial to the midpoint of its range (5.00).
3.
Adjust the decade resistance box until the magnitude of the voltage on the multimeter is as
close to zero as possible.
4.
Now go back to the potentiometer and adjust the potentiometer until the voltage reading on the
multimeter reads zero (or as close to zero as possible). The bridge is now balanced, and points C
and D in the bridge circuit are at the same potential. This means that you are now able to find
the value of the unknown resistance in terms of the other three resistances. (See section I-E
above.)
5.
Record the material, gauge number, and length of the unknown resistance, the decade
resistance box value, and the potentiometer reading.
6.
Repeat the above measurements for the remaining two unknown resistance values and record
the necessary data. The diameters of the wire for given B&S gauge numbers and the resistivity
values can be found in the “Handbook of Chemistry and Physics.”
4
B.
Data:
Unknown Resistance
Material
Gauge
No.
Diameter
(m)
Length (m)
Decade
Resistance
(
Potentiometer
Reading
(10.00 –
Potentiometer
Reading)
C.
Use the information above to determine the resistivity of the materials from which the unknown
resistances are made. Show your calculations below.
D.
Report the experimental values of resistivity, the book values, and the percentage error in a table.
Material
Experimental
Resistivity (-m)
Theoretical
Resistivity (-m)
Percentage Error
5
E.
Extra Credit:
If the potentiometer was set at 1.00 or 9.00 instead of 5.00 in step III-A-2 above, the error in the
experimental value will most likely be larger. Explain why? (Hint: What is the total fractional
uncertainty in the potentiometer readings if there is an uncertainty of 0.05 in the potentiometer
reading? Compare the fractional uncertainties when the potentiometer readings are 5.00 and 5.00 (=
10.00 - 5.00) to when the potentiometer readings are 1.00 and 9.00 (= 10.00 – 1.00) dial is set at 5.00.
6