CU-Boulder PHYS 3330 - DC Measurements, Voltage Dividers, and Bridges

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Physics 3330 Experiment #2 Fall 2006 DC Measurements, Voltage Dividers, and Bridges Purpose You will gain familiarity with the circuit board and work with a variety of DC techniques, including the Wheatstone bridge and 4-terminal measurement techniques. Readings H&H Section 1.03, 1.04, 1.05. Optional: Diefenderfer 1.9-1.13, 6.8-6.11 Theory 1. The Basic Wheatstone Bridge Bridge circuits are used to precisely compare an unknown impedance with a standard. The simplest example is the Wheatstone bridge (Fig. 2.1), a four-arm bridge with a resistor in each arm, which is usually used at DC or low frequencies. It has many applications in measurement circuits, where often the unknown resistance Rx is a resistive sensor, such as a platinum thermometer or a mechanical strain gauge (see H&H 15.03). There are other types of bridges, including AC bridges with capacitors or inductors in one or more arms, radio-frequency bridges, and bridges that use precision transformers to generate voltage ratios. In our the basic bridge Rx, Rs, R1, and R2 are each >>0.1Ω so that all contact resistances can be ignored. The bridge is made from two voltage dividers, each connected to the same source voltage ε. R1 and R2 are formed by a 10-turn potentiometer. When the division of the two dividers is adjusted to the same value the null meter reads zero voltage (ΔV=0). This occurs when Rx/Rs = R1/R2 , a formula which can solved for the unknown resistor Rx in terms of the standard Rs and the ratio R1/R2. Fig. 2.1 a) Basic Wheatstone bridge. b) Thevinin equivalent circuit. =10k Ω =SRP=(1-S)RPRxNull-meter RS ε+_ Voltage Source }R210-turn potentiometer RP1RStandard Unknown BΔ V (a) A}_ε+ΤRT ΔVBA(b) Experiment #2 2.1 Fall 2006More generally, the operation of the bridge, both in the balanced and the unbalanced states, follows directly from its Thévenin equivalent and the equations: . ,2121211RRRRRRRRRRRRRRRsxxsTsxxT+++=⎟⎟⎠⎞⎜⎜⎝⎛+−+=εε Stare at these equations for a while and try to see why they are correct without doing any calculations. 2. Four-terminal Connections Typically, when we wish to measure the resistance of an element we can simply connect the element between the two leads of a DMM and read “Ohms”. With the modern digital DMM this works quite well unless the resistance of the element to be measured is small - not very much higher than the resistances of the leads or contact resistances between the sample and the leads (probably less than an ohm for your leads). If the element’s resistance is not much higher than the leads, then the lead resistance will make a sizeable impact on the measurement, skewing it badly. The way around this is to use the method of 4-terminal connections, in which the current leads are separate from the voltage leads. A schematic is shown in Figure 2.2. A known large current passes into and out of the sample from CT.1 to CT.2. The voltage across the sample is measured at VT.1 and VT.2. Since there is essentially no current flowing through VT.1 and VT.2 there is also no voltage drop across them, even if they are of a sizeable resistance. Ohm’s law is then used to determine the resistance of the sample. The black dots CT.1 and CT.2 represent the current terminals through which current flows into and out of the sample. The arrows VT.1 and VT.2 represent voltage terminals to which the voltmeter is attached using spring loaded alligator clips. The sample length is the distance between the voltage terminals. Note that the contact resistance (about 0.1Ω) of the voltage terminals can be neglected since it appears in series with the 10 MΩ resistance of the DMM. Also, the current terminals CT.1 & CT.2 are outside the voltmeter circuit. This is so that the voltage drops in these contacts will not be measured by the voltmeter. Experiment #2 2.2 Fall 2006DC Power Supply+_RxSmall Alligator ClipsVoltmeterVT.2VT.1AmmeterCT.1CT.2Circuit boardI04-Terminal LayoutVT.1VT.2CT.1CT.24-Terminal SymbolRx Fig 2.2 4-Terminal Connections: Physical and Schematic New Apparatus and Methods PROTOTYPING BOARDS Your instructor will give your team a prototyping board to use for building your projects. Write your team member’s names on it. Your team will use the same board all semester. An incomplete experiment can be left on the board and finished later. Store the board on the shelf labeled for your section. Components (resistors, capacitors, transistors, etc.) are available from the community stock. Take what components you need for the experiment. When it is over, stick them in a piece of foam or store them in a cardboard box for future use until the end of semester. Do not take a new component for an experiment unless you don't have it already. The complete circuit board contains a front panel, and a plug-in circuit board. On the front panel, you will find: • BNC cable sockets that carry electric signals between your circuit on the board and the function generator and oscilloscope. • Colored banana jacks to bring in dc power for transistors or chips from an external power supply (+15 V red, -15 V blue, +5 V orange, and 0 V black). • A precision 10 kΩ ten-turn potentiometer (linearity ± 1/4%), and several switches. • A wire or component on the board might be broken, or might break during the semester. Don’t worry – you will be able to repair the board as you go. Experiment #2 2.3 Fall 2006The circuit board contains arrays of holes, interconnected by buried conductors, into which components are plugged to build your circuit. The description we give below is generally accurate, but there are several varieties of boards in the lab; use the multimeter to verify the connections inside your board. In general, you can never be sure that any two contacts are really connected, or any wire is really continuous, unless you test it yourself, so get into the habit of testing things. Figure 2.3 DC Power Connection for the Power Supplies+ – gnd. + – gnd. redblueblack+15–150 V+15 –15 0 V 0 V V I I V Power Supply Circuit Board • The long lines of connected holes are used for power lines (+15 V red and -15 V blue) and ground lines (0 V black). They are never used for signals. • The 5 holes in each short group at right angles to the long lines are interconnected, but separate from every other group of 5. A given short group is used to make the junction between two or more components


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CU-Boulder PHYS 3330 - DC Measurements, Voltage Dividers, and Bridges

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