Exp_2_fa09 - Physics 3330 Experiment #2 Fall 2009 DC...

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Physics 3330 Experiment #2 Fall 2009 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 the 4-terminal resistance measurement techniques. Reading: H&H Section 1.03, 1.04, 1.05. 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 R x 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 R x , R s , R 1 2 are each >>0.1 so that all contact resistances (typically of order .1 ) can be ignored. The bridge is made from two voltage dividers, each connected to the same source voltage ε . When the division of the two dividers is adjusted to the same value the null meter reads zero voltage ( V=0). This occurs when R x /R s = R 1 /R 2 , a formula which can solved for the unknown resistor R x in terms of the standard R s and the ratio R 1 /R 2 . Fig. 2.1 a) Basic Wheatstone bridge. b) Thevinin equivalent circuit. (b) A B ε _ + Τ R T V } 2 =10k =SR P =(1-S)R P R x Null-meter R S ε + _ Voltage Source } R 10-turn potentiometer R P R 1 Standard Unknown B V (a) A Experiment #2 2.1 Fall 2009
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More generally, the operation of the bridge, both in the balanced and the unbalanced states, follows directly from its Thévenin equivalent and the equations: . , 2 1 2 1 2 1 1 R R R R R R R R R R R R R R R s x x s T s x x T + + + = + + = ε 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 a circuit 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. DC Power Supply
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This note was uploaded on 11/10/2009 for the course PHYS 33 at Colorado.

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Exp_2_fa09 - Physics 3330 Experiment #2 Fall 2009 DC...

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