The voltmeter shown in the figure below can be modeled as an ideal voltmeter (a
ID: 2145124 • Letter: T
Question
The voltmeter shown in the figure below can be modeled as an ideal voltmeter (a voltmeter that has an infinite internal resistance) in parallel with a 12.0-M? resistor. Calculate the reading on the voltmeter for the following.
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The voltmeter shown in the figure below can be modeled as an ideal voltmeter (a voltmeter that has an infinite internal resistance) in parallel with a 12.0-M? resistor. Calculate the reading on the voltmeter for the following. (f) What is the largest value of possible if the measured voltage is to be within 10 percent of the truevoltage (i.e., the voltage drop across R without the voltmeter in place?) I give priority to first correctly answered question. I can't give everyone the five stars for effort that I wish I could. Good luck!Explanation / Answer
a) so first combine R with voltmeter in parallel
1/R1 = 1/R + 1/Rvolt
R1 = R Rvolt/(R + Rvolt)
so R total = 2R + R Rvolt/(R + Rvolt)
I = V/R = 10/(2R + R Rvolt/(R + Rvolt))
so Voltmeter will read = R1*I
= R Rvolt/(R + Rvolt)*(10/(2R + R Rvolt/(R + Rvolt)))
= 1.2E3*12.0E6/(1.2E3+12.0E6)* (10/(2*1.2E3+1.2E3*12.0E6/(1.2E3+12.0E6)))=3.33311
b)
11.1E3*12.0E6/(11.1E3+12.0E6)* (10/(2*11.1E3+11.1E3*12.0E6/(11.1E3+12.0E6)))=3.331
c)
0.9E6*12.0E6/(0.9E6+12.0E6)* (10/(2*0.9E6+0.9E6*12.0E6/(0.9E6+12.0E6)))=3.1746
d)
9.4E6*12.0E6/(9.4E6+12.0E6)* (10/(2*9.4E6+9.4E6*12.0E6/(9.4E6+12.0E6)))=2.190
e)
94.0E6*12.0E6/(94.0E6+12.0E6)* (10/(2*94.0E6+94.0E6*12.0E6/(94.0E6+12.0E6)))=0.5357 V
f) without voltmeter should be R 10/3R = 10/3
so
|V with - Vwithout}/Vwithout = 0.1
so
10/3-R*12.0E6/(R+12.0E6)* (10/(2*R+R*12.0E6/(R+12.0E6))) = 0.1*10/3
solve for r
R=2.0E6 ohms
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