The voltmeter measures the voltage across a component

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Unformatted text preview: refore connected in parallel with the component. As shown in the dashed box in Figure 2.1, the voltmeter consists of a d’Arsonval movement in series with a resistor whose internal resistance is deliberately made very large to minimize the current drawn from the circuit. Rm represents the total resistance of the meter. Establish a set of ALTERNATIVE solutions and determine the one that promises the greatest likelihood of success. To show the effects of the internal resistance of a real voltmeter, (a) find VR 2 if R m is an open circuit, and (b) find VR 2 if R m is a short circuit. ATTEMPT a problem solution. Using voltage division, R2 Rm VS VR 2 = R 1 + (R 2 R m ) lim VR 2 | v v (a) R m →∞ | R2 Rm ( R12 + R1m ) -1 R2 VS = lim = lim VS 1 1 -1 VS = R m →∞ R + R R m →∞ R + ( R1 + R 2 1 R2 + Rm ) 1 2 Rm e-Text Main Menu | Textbook Table of Contents | Problem Solving Workbook Contents lim VR 2 (b) R m →0 R ( R 2+R m ) RR 0 2 m 2 Rm VS = VS = lim = lim VS = 0 RR R m →0 R + R R m →0 R + ( 2 m ) R1 + 0 1 1 R 2 +R m 2 Rm EVALUATE the solution and check for accuracy. (a) If R m = ∞ (open circuit), then all the current flowing through R 1 will continue [ through R 2 . Clearly, using voltage division, VR 2 = R 2 (R 1 + R 2 ) VS (b) If R m = 0 (short circuit), then no current will flow through R 2 and VR 2 = 0 . This makes sense due to the fact that current flows through the path of least resistance. Has the problem been solved SATISFACTORILY? If so, present the solution; if not, then return “ALTERNATIVE solutions” and continue through the process again. This problem has been solved satisfactorily. If Rm >> R2, the internal resistance will only slightly effect the circuit. As the value of Rm approaches R2, the effect of the internal resistance becomes increasingly more significant. [2.55] As a design engineer, you are asked to design a lighting system Problem 2.19 consisting of a 70 W power supply and two light bulbs as shown in Figure 2.1. You must select the two bulbs of the following three available bulbs. R 1 = 80 ohm...
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This note was uploaded on 07/16/2012 for the course KA KA 2000 taught by Professor Bkav during the Spring '12 term at Cambridge.

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