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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 eText 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.
 Spring '12
 bkav

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