Voltage query -- A power supply, resistors and a voltmeter....

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A 12V DC supply is connected across two 100k ohm resistors in series, with a voltmeter of 10,000 ohms per volt set to the 10V range measuring one resistor. The total resistance of the circuit, including the voltmeter in parallel with one resistor, is calculated to be 150k ohms. The voltage reading across the resistor is determined to be 4V, while the ideal voltage without the meter would be 6V. The percentage error in the meter reading is calculated to be approximately 33.33%. The discussion emphasizes the importance of using correct formulas and understanding circuit analysis principles, such as Kirchhoff's laws.
  • #31
ok battery voltage/total resistance x R2= voltage across r2

12v / 150k ohms x 50k ohms = 4 V
 
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  • #32
alsy said:
ok battery voltage/total resistance x R2= voltage across r2

12v / 150k ohms x 50k ohms = 4 V
Yes! Well done.

So the meter will read 4 V. That answers part 2 of the question. Now, how will you address part 3?
 
  • #33
thank you.

ok part 3.

10,000ohms sensitivity x 4v= 40,000 /10v range = 4000 / 100= 40%
 
  • #34
I think what they're looking for is the percent error in the measured value when compared to what an ideal meter would read (that is a meter which would not affect the circuit operation at all, one with infinite ohms per volt sensitivity).

What would the voltage be across R2 if the meter was not attached?
 
  • #35
12v / 200k ohms x 100k ohms = 6v voltage across r2 without meter
 
  • #36
alsy said:
12v / 200k ohms x 100k ohms = 6v voltage across r2 without meter
Great. So given that the meter reported the voltage as 4 V, what's the percent error in the reading?
 
  • #37
4v / 6v = 0.66 x 100 =66.6% error
 
  • #38
alsy said:
4v / 6v = 0.66 x 100 =66.6% error
No, that's the percentage of the "true" voltage that's seen. What you want is the percentage that the error in the reading represents.

What's the formula for percent error (or percent difference)?
 
  • #39
percentage error formula

accepted - measured / accepted x 100
 
  • #40
alsy said:
percentage error formula

accepted - measured / accepted x 100
Yup. Again, get in the habit of using parentheses to clear up operation precedence vagueness in your formulas:

[(accepted - measured) / accepted] x 100
 
  • #41
sure

[( 6v -4v /6 x 100 = 33.33 %
 
  • #42
Looks good. Keep in mind that they may want to know the "direction" of the percentage error, indicating this with a sign. So if the measured value is 33.3% low, then it might be written as -33.3%. If this is a written hand-in assignment then you can use the sign method or make an appropriate annotation on the value to indicate your understanding that it is a "low reading" of the true value.
 
  • #43
ok but if they say percentage error then I just express as 33.33%
 
  • #44
alsy said:
ok but if they say percentage error then I just express as 33.33%
As I said, it depends upon who's looking at the result and how you've been taught to present a percent error. Certainly the magnitude of the error is 33.3%. If that's all they want to see, then that's fine.
 
  • #45
ok thanks.

I have a shorter engineering science related question,regarding linear velocity.not sure if that's your area or if it can be answered here
 
  • #46
alsy said:
I have a shorter engineering science related question,regarding linear velocity.not sure if that's your area or if it can be answered here
Always start a new thread for a new question/topic.
 
  • #47
ok thanks
 

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