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Title: Students will provide an appropriate title to a self-designed laboratory experiment based on ideas and knowledge they acquired from their previous laboratory experiments. Objectives Using background information on circuit analysis, in this experiment students will be simulating a circuit comprised with at least 5 resistors, 2 sources, and/or capacitor(s), and/or inductor(s). The simulated results then be compared with calculated (theoretical) results and also be presented. Task The experiment should be designed keeping these information in mind: The circuit diagram will include at least 5 resistors, 2 sources, and/or capacitor(s), and/or inductor(s). A formal lab report for the experiment. ● A group presentation for result analysis and comparision ● ● Lab Report The lab report should include the following sections: Objectives This is a summary statement of the work to be accomplished in this experiment. An overall direction for laboratory investigation, the obtained result and summary of conclusions must be provided. Equipment A list of all the apparatus used in the experiment should be included. A detailed and labeled diagram to illustrate the setup of the experiment Procedure Explain step-by-step procedure in a numbered sequence so that other learners can comprehend the experiment and be able to reproduce the experiment by reading your procedure.
THE WHEATSTONE BRIDGE AND RESISTIVITY Objective: To determine the resistivity of a nickel silver wire and to measure an unknown resistance using a Wheatstone bridge circuit. Apparatus: Slide-wire Wheatstone bridge, digital multimeter, analog ammeter, galvanometer, DC power supply, unknown resistor, decade-resistor box, connecting wires and alligator clips. Theory: Resistivity: For Ohmic materials such as metallic conductors, the resistance it offers to the flow of electrical charge is given by: R-p² where L, A, and p are the length, cross-sectional area, and resistivity of the resistor, respectively. This equation shows that an increasing length of material will offer more resistance, while a larger cross- sectional area will result in less resistance to current flow. The resistivity can be expressed in units of 2.m, and for metals, is typically on the order of 1072 m. The resistivity of the conductor depends only on the material composition of the resistor and its temperature. For metals, the hotter the material is, the greater its resistance. The Wheatstone bridge circuit: The Wheatstone bridge is a very sensitive circuit that can be used to find the resistance of a particular resistor, Ru, by comparing it with a known resistor, RK. In practice, it is most commonly used in control circuits to detect changes in resistance that may trigger another electronic device. For example, the resistance of a resistor in an oven will increase in temperature as the oven is heated; this change in resistance is detected by the Wheatstone circuit (which becomes unbalanced), and triggers the control to the heater in order to maintain a temperature that is set by the user. The circuit consists of four resistors connected in the form of a square, and a galvanometer across one diagonal and voltage source across the other, as shown in figure 1. A galvanometer is a very sensitive ammeter that has negligible resistance. The Wheatstone bridge circuit is said to be balanced if no current runs through the galvanometer. We can see this by applying Kirchhoff's circuit rules. The junction rule is a restatement of the conservation of charge. Thus, the current, I, branches at point A in the circuit. Some of it, I will travel to point C, and the other part of the current travels toward D. The part that travels along the path to D must therefore be I-I₁. At point D, the current branches again: part can go through the galvanometer, IG, and part can continue to point B, which will be I-I₁-IG. Currents IG and I₁ flow into point C, so the current along path CB must be I+IG. Finally, at point B, the currents recombine, so I₁+ IG and I-1₁-IG sum to the total current I that travels back to the power supply. A (1) I 1-1 Ru R₁ C D RK I₁+IG B WWW 1-11-IG Figure 1. Wheatstone Bridge
UTC Physics 1040L Wheatstone Bridge and Resistivity Kirchhoff's loop rule may also be applied to this circuit. The loop rule is an application of the energy conservation principle to the electric potential that exists at various places in a circuit. It states that for a closed circuit loop, the total of all the potential drops is the same as the total of all the potential rises, where V is either a voltage source like a battery, or can be found by Ohm's law. In a balanced Wheatstone bridge, no current will flow through the galvanometer. Remember that current will flow between two points if the two points are not at the same electrical potential, V. Examination of the circuit diagram in Figure 1 reveals that current at point A is divided, so that some goes toward point D and some goes toward point B. If point D and point B are not at the same potential, some current will cross the bridge at the galvanometer. Therefore, the voltage drop (equal to the current times the resistance) from point A to point C must equal the voltage drop from point A to point D. Similarly, the voltage drops must be equal across the paths CB and CD. This means that: I₁RU = (I-II)R₁ and (I₁+IG)RK = (I-1₁-IG)R₂ If we recall that in this case, IG = 0, and we divide the first equation by the second equation, then: RU R₁ RK R₂ or RU 2. Adjust the power supply to output between 1-2 V. Examine your ammeter to ensure you know how to read the scale. If you are on the 500 mA scale, this reading is the maximum deflection of the meter. In practice, we will use the slide wire as both R₁ and R₂, dividing it into two resistors by making a contact with the galvanometer branch at some point on the wire. Since the resistance is directly proportional to length, the unknown resistance, Ru may be found by taking the ratio of the lengths of the two pieces of wire and multiplying it by the known resistance, RK: L₁ (1-L₁) RU = RK O R₁ -RK. R₂ Procedure and Data Analysis: PART I. Determining the resistivity of the slide wire. 1. To determine the resistivity of the slide wire on the Wheatstone bridge, you will determine its resistance as a function of length. Set up the circuit in Figure 2. You will use the analog ammeter, and a digital multimeter for the voltmeter. Pay attention to the scale your ammeter is set to read on. Hook the power supply and ammeter to the circuit. Use the connecting wires with banana plugs to connect the voltmeter directly across the circuit and the slide wire. Rev. 01/15 KBW Figure 2. Set up and circuit diagram for part 1. DC supply Digital multimeter (2) Ammeter 3. Slide the movable contact all the way to the end, so that there will be only 10 cm of wire when you depress the contact in order to complete the circuit. Do not hold down the contact as you move it - doing so will cause the wire to become misshapen and non-uniform in its cross-sectional area. Experiment Description - Page 2 of 4 movable contact slide wire
Wheatstone Bridge and Resistivity 4. Depress the contact to close the circuit where 10 cm of wire will be included as the resistor in the circuit. Note there should now be current through the circuit and the ammeter should be reading a value. Also note that the voltmeter no longer reads the value you are supplying. UTC Physics 1040L 5. Take readings of the current and voltage when the circuit includes lengths of 0.1 -0.9 meters of the wire, every 10 cm. Pay attention to the units and record your data on your data sheet. 6. Calculate the resistance for each length of wire using Ohm's Law (V = IR), and show a sample of this calculation on your data sheet. 7. Make a graph of Resistance (on the y-axis) vs. Length (on the x-axis). By equation (1), the theory predicts a linear regression. Find the slope of the line, which should represent p/A (in units of 22/m). Label your graph appropriately and print it to include with your report. 8. Calculate the cross-sectional area of the wire by assuming it is a 30-gauge wire (AWG), which corresponds to a circular diameter of 0.25 mm. Express the area in m². Remember that the area of a circle is r². 9. Using the slope of the fit to your data and the cross-sectional area of the wire, calculate p. Show this calculation and the above indicated ones on your data sheet. PART II. Finding the resistance of an unknown resistor using the Wheatstone bridge. 1. Connect the Wheatstone Bridge circuit as shown in Figure 3, but do not turn the power supply on yet. You should verify that this is the same as the circuit diagram shown in figure 1. The decade resistor box will serve as your known resistor, RK. It is adjustable and can be set to any value from 1 to 999922 in 12 steps. You will be able to turn the dials to different values of RK, and when you find a match that is close with Ru, there will be very little current flowing through the galvanometer. Ru A Rev. 01/15 KBW Galvanometer R₁ R₂ DC supply ROOOO B Figure 3. Set up for part 2. 2. Set the resistance on the resistor box to equal at least 10 Ohms before turning on the power supply. This will serve to limit the current in the bridge, which could overheat the components. Your unknown resistor has more than 10 Ohms resistance. Turn on the power supply and adjust it to between 1 and 2 V. 3. Position the movable contact on the meter stick near the middle and make contact with the wire. The galvanometer needle should deflect. Now increase the resistance of RK by turning the dials on the box. You want to do this in an incremental fashion. When you find the resistance that is similar to Ru, the needle on the galvanometer will read near 0 μA. 4. Now balance the bridge exactly. Do this by adjusting the position of the movable contact a few centimeters to the right or left. This changes the resistances for R₁ and R₂ because you are