Download WHEATSTONE BRIDGE

WHEATSTONE BRIDGE
Objective:
To study the Wheatstone bridge and its capabilities for the accurate measurement of voltage and
ammeters across resistances
Equipment:
slide wire with movable contact, resistance boxes, galvanometer, switch, power supply, unknown
resistances
Introduction:
Ordinary voltmeters and ammeters are not in general of high accuracy. More accurate
measurements are made with circuits that contain precision resistance elements. These circuits
utilize a galvanometer to detect a null or zero current condition of balance. One such circuit is the
Wheatstone bridge used for the measurement of resistance and capable of high accuracy.
X
In the circuit shown in the figure, R3 and RG
are resistance boxes; X is an unknown
resistance from the board; R1 and R2 are the
resistances of the slide wire on each side of
the movable contact and are length L1 and
L2 respectively. G is the galvanometer, E is
the 12-volt D.C. output of the power supply,
and S is the switch.
R3
G
R1
L2
L1
S
Wire
R2
E
In the circuit operation R3 functions as a standard resistance to which the unknown X is
compared.
At the balance condition of zero (no galvanometer deflection) the ratio of X to R will equal the
ration of R1 and R2. This is measured as the ration of L1 and L2, which is read directly from the
meter stick on which the slide wire is fastened. Thus the measurement does not relate to any
meter reading. Its accuracy depends only on the accuracy of the resistance elements involved.
It is important that the value of R3 be selected of the same order of magnitude as X to insure that
the balance point on the slide wire occurs in the central region of the scale; otherwise the
accuracy will be poor. (The slide wire is most sensitive in the center area.)
Procedure
Part A
Connect an unknown resistor in the circuit as X. Adjust the resistance box RG to 1000 ohms.
(This protects the galvanometer when the bridge is not balanced.) Adjust R3 to the appropriate
value.
For resistor A set R3 to 3000 ohms,
For resistor B set R3 to 1000 ohms,
For resistor C set R3 to 200 ohms,
For resistor D set R3 to 100 ohms,
For resistor E set R3 to 20 ohms,
For resistor F set R3 to 10 ohms.
Adjust the power supply for 3 to 4 volts at E with the switch closed.
In making measurements, leave S and the contact on the slide wire open, except for brief periods during
which measurements are made.
Depress S and then the slide wire contact. Observe the galvanometer deflection and immediately open S
and the slide wire contact. Move the adjustable contact to a different position on the slide wire and repeat.
Continue the adjustment of the slide wire until zero deflection of the galvanometer is obtained*.
Next set RG to zero resistance. This now utilizes the full sensitivity of the galvanometer.
Make additional small adjustments as needed for a final balance (no deflection) at high sensitivity.
*It is possible that the needle will not fall on “the zero” of the galvanometer. You may adjust the needle if
you want but it is not necessary. What is important is that there is NO movement of the needle when the
slide wire key is depressed. If the needle moves then the bridge is not balanced.
Record L1 and L2 from the meter stick on which the slide wire is mounted. Note that L1 occurs on the
same side of the bridge circuit as the unknown X and L2 is on the side with the resistance box R.
Switch RG back to 1000 ohms to protect the galvanometer.
Repeat the procedure for the rest of the unknown resistors. Remember to change R3 to correspond to the
unknown being tested.
Calculate all resistances (A-F) from the slide wire measurements by the relation
X = R3(L1/L2)
Part B
Traditionally resistors are coded with colored stripes that indicate their resistance. The first three stripes
give the value of the resistance while the fourth is the tolerance. For us tolerance means the error or
percent uncertainty. The colored bands are given in the table below. The first two bands give the
numerical value, the third band gives the multiplier (power of ten), and the fourth band is tolerance.
Occasionally there is a fifth band, usually a yellow. This band marks the right hand end of the resistor. It
has no numerical value. The bands are read from left to right. If the resistor has no yellow fifth band then
the end that is closest to a colored stripe is the left end.
Enter the color code values in the data table.
Calculations
Each measurement of L1 and L2 will be uncertain to some extent.
A value of one half of .1 cm is reasonable.
If L1 is too large by .05 centimeters then surely L2 is too small by .05 centimeters.
Since you divide one by the other to obtain X the overall uncertainty is compounded.
Generally the uncertainty due to the wire itself is .2%.
This can be seen by propagating the uncertainties using “Rule 3”.
Let R3 = 3000  1 
L1 = 38.00  .05 cm
L2 = 62.00  .05 cm
X = R3 (L1/L2) = (3000)(38/62)  = 1839 
X / X = ((R3 / R3)2 + (L1 / L1)2 + (L2 / L2)2)1/2
= ((1/3000) 2 + (.05/38) 2 + (.05/62) 2) 1/2
= ((1.11x10-7) + (1.73x10-6) + (6.50x10-7)) ½
= (2.49…x10-6) ½ = .0015789 (and lots more digits)
(that’s .2%)
X = X(0.0015789) = (1839 )(0.0015789) = 2.9035…  3 
X = 1839  3 
Determine the uncertainty of the resistance for each unknown, X, both in % and in ohms.
Compare the experimental slide wire resistance to the color code resistance by calculating the percent
error for each unknown.
%err = [ abs(Xslide – Xcolor) / Xcolor ]  100%
Color Code Table
Band 1
Black
=0
Brown = 1
Red
=2
Orange = 3
Yellow = 4
Green = 5
Blue
=6
Violet
=7
Grey
=8
White = 9
Band 2
Black = 0
Brown = 1
Red
=2
Orange = 3
Yellow = 4
Green = 5
Blue
=6
Violet = 7
Grey = 8
White = 9
Band 3
Black = 1
Brown = 10
Red
= 100
Orange = 1000
Yellow = 10000
Green = 100000
Blue
= 1000000
Violet = 10000000
Grey = 100000000
White = 1000000000
So, if a resistor has bands that are:
Orange (3), Green (5), Red (100), Gold (5%)
it is 35 x100 
= 3500  5% 
= 3500  175 
= 100
= 101
= 102
= 103
= 104
= 105
= 106
= 107
= 108
= 109
Band 4
Gold = 5%
Silver = 10%
Fat Red = 2%