Electrical Circuits, V

Bridge Circuits

I. Bridge Circuits

A bridge circuit can be used to make an accurate determination of the value of an unknown circuit element. When the unknown circuit element is a resistance, the bridge is a Wheatstone bridge.

A. A circuit is set up with four resistors and a battery as shown. What can you say about the magnitude of the current passing through both R1 and R2?

B. What can you say about the magnitude of the current passing through both R3 and 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?

D. A resistor R is connected between points C and D to create a bridge circuit. In order for no current to flow through the resistor R, how must the voltages at points C and D be related? Explain.

When no current flows through resistor R, how must the currents I1 and I2 be related? How about currents I3 and I4? Explain.

When no current flows through resistor R, how must the voltages VAC and VAD be related to each other, and VCB and VDB be related to each other? Express the relationships in terms of current and resistance.


E. When the conditions described in part D exist in the bridge circuit, then a simple relationship can be found that relates the resistances R1, R2, R3, and R4. In the bridge circuit, three of the resistances are known and the fourth is determined through the simple relationship. For example, suppose resistances R1, R3, and R4 are known. Then the fourth resistance R2 is given by the relationship .

Rewrite the equations for the relationships you noted in the previous section. Show how these equations can be mathematically manipulated to give the expression for R2 above.

II. Bridge Construction – the elements

A. Examine the DC power supply. Look at the face of the supply and figure out how to turn it on and how to use the meter on the DC power supply to read voltage values and current values. The power supply acts like a battery except that chemical reactions are not producing 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. What are some of the electrical quantities it can measure? Where do you plug in the probes in order to measure DC voltage? AC voltage? DC current? AC current? Resistance? Capacitance?

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 potentiometer. This is important!

Set up your multimeter to measure resistance. Connect the probes of the multimeter to binding posts A and B on the potentiometer. Record the value of resistance. How does the resistance change when the potentiometer knob is turned?

Connect your multimeter to posts A and C, and again observe how the resistance changes when the knob is turned. Can you come up with a relationship between the potentiometer reading and the resistance reading of the multimeter? (Think about proportion.) What is the relationship?

Now connect your multimeter to posts B and C, and observe that no matter what the setting is on the potentiometer, the resistance from B to C plus the resistance from A to C equals the resistance from A to B. This means that RAC is directly proportional to the potentiometer reading and RBC is directly proportional to (10.00 – potentiometer reading).

Draw a diagram of what you think the inside of the potentiometer looks like.

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 five leads (wires with banana plugs) and two probe leads 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).

A. 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 reading to the midpoint of its range (5.00).

3. Adjust the decade resistance box until 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. 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.)

5. Record the material, gauge number, and length of the unknown resistance, the decade resistance box value, and the potentiometer reading.

Repeat the above adjustments 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.”

Data:

Unknown Resistance / Decade
Resistance (W) / Potentiometer
Reading / (10.00 –
Potentiometer Reading)
Material / Gauge No. / Diameter
(m) / Length (m)

B. Use the information above to determine the resistivity of the materials from which the unknown resistances are made. Show your calculations.

C. Report the experimental values of resistivity, the book values, and the percentage error in a table.

Material / Experimental Resistivity (W-m) / Theoretical Resistivity (W-m) / Percentage Error

D. If the potentiometer was set at 1.00 or 9.00 instead of 5.00 in step A2 above, the error in the experimental value will most likely be larger. Why? (Use another sheet of paper to answer this question.) (Hint: How much uncertainty is produced for the unknown resistance value if there is an uncertainty of 0.05 in the potentiometer reading when the dial is set at 5.00? How will the same uncertainty affect the unknown resistance value when the potentiometer reading is 1.00? How about if the reading is 9.00?)

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