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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