Q#776: [Current of Electricity] (Past Exam Paper – June 2014 Paper 11 Q33)
In circuit below, a voltmeter of resistance RV and an ammeter of resistance RA are used to measure the resistance R of the fixed resistor.
Which condition is necessary for an accurate value to be obtained for R?
A R is much smaller than RV.
B R is much smaller than RA.
C R is much greater than RV.
D R is much greater than RA.
Solution 776:
Answer: A.
To obtain the resistance of resistor R from the set-up shown, the potential difference and current flowing through the resistor are measured.
Ohm’s law: V = IR
Resistance = V / I
(Voltmeter and ammeter cannot give resistance on their own. Resistance should be calculated.)
Ideally, a voltmeter should have an infinite resistance and is connected in parallel to the component being investigated. This is to avoid a large current to flow through it. Current is highest when the resistance is smallest.
Ideally, an ammeter should have negligible resistance and is connected in series to the component being investigated so that it does not affect the value of the current flowing.
This, RV should be very large (larger than R) and RA should be very small (smaller than R). Hence, the necessary condition for an accurate value to be obtained for R is than R is much smaller than RV.
The voltmeter must have much greater resistance than R, otherwise there will be significant current in voltmeter and the value obtained from V/I will not be an accurate value for R.
However: If the statement "RV should be very large (larger than R) and RA should be very small (smaller than R)" is true, then surely both A and D are correct options?
The idea is that If Rv is too small then the current flows through V and the ammeter reading is not only measuring the current through R. Therefore the equation R=V/I cannot do this as although it is the correct V it is not the I through resistor R - it is instead the current through V and R.
However, if RA is large this will have no effect as both I and V will change. Whatever the value of RA, the voltmeter is only across R and will only measure the V across R. And as the ammeter is in series with R, the ammeter will always measure the current through R. Using R = V/I will give the resistance.
If RA is large both V and I in R=V/I decrease proportionally and R wouldn't change.
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