# Physics 3330 Experiment #2 Fall DC techniques, dividers, and bridges

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1 Physics 3330 Experiment #2 Fall 2002 DC techniques, dividers, and bridges Purpose You will gain a familiarity with the circuit board and work with a variety of DC techniques, including voltage dividers, the Wheatstone bridge, and 4-point measurement techniques. You also will gain a familiarity with the concept of input and output impedance. eadings D&H , Theory 1. The Basic Wheatstone Bridge Prior to very accurate DVM s, the Wheatsone bridge was widely used to determine an unknown resistance x by comparison with a precisely known standard s. It s operation illustrates many principles of DC circuits. In the basic bridge x, s, 1, & 2 are each >>0.1Ω so that all contact resistances can be ignored. 1 and 2 are the opposite legs of a potentiometer and can be continuously and accurately varied, until the null meter reads no current or voltage. Then, according to voltage divider rules, s/(sx) = 2/(12) and so x can be determined. Null-meter ε _ Voltage Source S x Standard B V Unknown (a) A } 2 =(1-S) P } 1 =S P P =10kΩ 10-turn pot. ε Τ _ (b) T B V A Fig. 2.1 a) Basic Wheatstone bridge. b) Thevinin equivalent circuit. Experiment #2 2.1 Fall 2002

3 DC Power Supply _ I 0 Voltmeter Ammeter Small Alligator Clips 4-Terminal Layout VT.1 x VT.2 Circuit board CT.1 CT.1 VT.1 x VT.2 CT.2 CT.2 4-Terminal Symbol Fig terminal connections: physical and symbolic New Apparatus And Methods CICUIT BOADS (see figure 2.3) Take a circuit board and write your name on it. You 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 are sure 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 k? ten-turn potentiometer (linearity ± 1/4%), and several switches. Experiment #2 2.3 Fall 2002

4 Vin V out BNC Connecto rs C L Banana Jacks DC Power 0 V Sw itch o tentio me te r Junctio n Strip V out V in C L p anel g round Figure 2.3 The circuit board contains arrays of holes, interconnected by buried conductors, into which components are plugged to build your circuit. 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 of your circuit. There are four color coded binding posts on the circuit board. They are wired to the assiciated banana jacks on the front panel. Good electric contact is essential when you plug in components or wires. Use only 22 or 24 gauge solid wire, not stranded wire. Push in each wire with thin nosed pliers until you feel the contacts grip. A common fault is to plug in enamel insulated wire, used for winding inductors. First burn off the enamel with a lighter flame for 1/2" at the end and clean with emery paper. Contact resistances should measure less than one third of an ohm. If you get confused about which holes are connected together by buried conductors, explore the board with an ohm meter. eliable ground connections (0 V), readily accessible from any point on the board, are essential to the good functioning of most circuits. The front panel is the ground for your circuit board since the coax cable shields connect the front panel of your circuit board to the ground of other instruments in your experiment. Experiment #2 2.4 Fall 2002

5 Problems - Turn these in to your instructor before the start of your lab! 1. Voltage dividers. An ideal voltage source drives current around the loop of resistors shown in Figure 2.4(a). Find a formula for the current I and the voltage Vout. What is Vout if V = 10 V, 1 = 1 kω, and 2 = 100 Ω? For these component values, what is the Thévenin equivalent circuit? Also calculate the voltage Vout for the modified circuit shown in Figure 2.4(b) with 3 = 200 Ω and the other components unchanged. What is the Thévenin equivalent circuit now 2. What is the diameter of a typical pure metal wire 6-ft long if its resistance is (at room temperature) is 0.1 Ω? Assume that the resistivity of typical pure metals at room temperature is about 2 x 10-8 Ω-m. What is the maximum error in measuring the diameter that you can tolerate if the resistivity is to have a 1% uncertainty? (a) V I I 1 2 Vout 0V 3. The American standard wire gauge gives a logarithmic measure of the diameter of a wire, AWG gauge = Log 10 (d/0.01"). (b) V 1 V out Wires usually are available only in even gauges. What gauge should you use for the 6-ft, 0.1Ω wire? 2 3 0V 4. Consider the basic Wheatstone bridge of Fig 2.2, Assume that the bridge has been balanced so that a resistance xo gives a potentiometer setting S o. Now leave the potentiometer alone, but let the Figure 2.4 Voltage dividers unknown resistance change by a small amount x. Show that, as a consequence, the null-meter will measure an (approximate) unbalanced potential difference V = ε ( x x 0 )1 ( S 0 )S 0 (3) What value of So gives you maximum sensitivity, V/ x? What does your answer imply about choosing a standard resistance if you know the approximate value of the unknown resistance? Experiment #2 2.5 Fall 2002

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