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Have your TA check your circuit diagrams to see if they are correct. 7 Wheatstone Bridge and Unknown Resistance The Wheatstone bridge is an electric circuit comprised of four resistors arranged in two parallel branches that are “bridged” by a voltage probe (as seen in Fig. 7). When a source voltage V S is applied across the circuit with arbitrary values of resistance, a voltage will develop V P across the bridge thereby driving a current I P through the voltage probe. By adjusting the values of resistance in either branch one can “balance” the circuit; this occurs when I P = 0 and therefore V P 0. At which point the four resistors have a specific mathematical relationship. By using a potentiometer (variable resistor) and an unknown resistor in one branch of the circuit one can varying the resistance until V P is approximately zero. Then, using the relationship determine the unknown resistance. You will now test this process. Figure 7: Wheatstone Bridge circuit. Prior to assembling your Wheatstone Bridge draw out the circuit diagram as in Fig. 7 with the variable resistor and unknown resistor in the same branch of the circuit. R A = ‘unknown’ R B = potentiometer 7

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R C = 1 k Ω R D = 100Ω Derive the relationship between the four resistors which leads to the bridge being balanced. Remember, this occurs when V P = 0, which means the midpoints of the two branches are at the same potential. Using the three resistors provided (values 100Ω, 1 k Ω and ‘unknown’) as well as the po- tentiometer mounted to the board, assemble the Wheatstone Bridge circuit on the Pasco Electronics Lab Board. Assemble the circuit such that its ends are connected to the two banana plug sockets located on the Electronics Board. The Pasco Voltage probe will act as the bridge; attach it between the two midpoints of the circuit’s branches. Attach the Power Amplifier to the two banana plug sockets, being aware of which is set to higher voltage. Turn the potentiometer to it’s maximum resistance value. Now that the circuit is config- ured, in the “Signal Generator” window in Data Studio set the power supply to output a DC voltage V S = 3 V . Set Data Studio to display V P in real time. While monitoring V P slowly decrease the resistance of the potentiometer so that V P 0. When V P = 0 then the bridge is “balanced”. With a multimeter measure the resistance of the potentiometer at which this occurs. Using this measured resistance and the previously derived mathematical relationship be- tween the resistors of the circuit, determine the value R x of the unknown resistor. To verify this remove the unknown resistor from the circuit and measure it directly using the multimeter. Compare the two values. You may be asking yourself “Why use the Wheatstone Bridge to find the resistance if one could simply measure it directly using a multimeter?” This is a good question and warrants consideration of the following: how does a multimeter go about determining resistance; what sort of difficulties might arise when measuring very small resistance values; is the Wheatstone Bridge method more accurate? With these in mind attempt to explain the usefulness of the Wheatstone Bridge. 8
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