The vertical amplifier of most oscilloscopes typically has an input resistance of 1MOhm and a calibration accuracy of 3% of full screen deflection. You want to use a scope to measure voltages in a variety of circuits yet limit loading by the scope to 3%. What is the highest output resistance of the circuits that you wish to measure that will remain within this load limit?

I originally thought I could solve the problem by setting up a voltage divider solving for R1 and R2 for example. Upon writing some equations down I ended up with an R^2 term thus a nonlinear relationship and I decided I am making things too complicated. Maybe I don't fully understand the question.

Does anyone have any suggestions?

 

Yes it's a simple voltage divider problem, so you determine what resistance in series with the 1 Mohm input will reduce the voltage by 3%.
Of course, worst-case, that can give an overall error in the measurement of 6%. Personally I would want to limit the loading error to less than 1% to maximize the overall accuracy.

 

Work backwards. You want to limit the error to 3%.

What value of R can you put in parallel with 1MΩ that will result in an equivalent resistance of 0.97R?

 

Work backwards. You want to limit the error to 3%.

What value of R can you put in parallel with 1MΩ that will result in an equivalent resistance of 0.97R?

I calculated about 32MOhm . . . But that doesn't seem right? If I set the parallel combination of 1MOhm and R equal to 0.97x1MOhm, thats the result I get for R . . .

 

Try again. You made a mistake somewhere.
Think about it.

1MΩ in parallel with 1MΩ would be 500KΩ.

1MΩ in parallel with 10kΩ would be close to 10kΩ to within 1%.

 

Ok, I think I was misinterpretting the problem. Instead of setting the parallel combo equal to 970k I wanted to set it to 3% of 1MOhm = 30K, in this case using the 1Mohm value given and the calculating the value of the circuit resistance I end up with about 30kOhm, which makes much more sense because in that case the circuit resistance is much less than the oscilloscope therefore the oscilloscope will have a small loading effect.

Thank you!

 

Or more precisely, no greater than 30.9kOhm . . .

 

You got it!

Now you can see how you can estimate this in your head.

10kΩ would be accurate to 1% with a 1MΩ scope probe.
20kΩ would be accurate to about 2%.
30kΩ would be accurate to about 3%.

Note that is approximate. It goes out of kilter as you go higher.