Again, since b and d are at the same potential, the
drop along dc must equal the
drop along bc. Thus,
Taking the ratio of these last two expressions gives
Canceling the currents and solving for R
x yields
This equation is used to calculate the unknown resistance when current through the galvanometer is zero. This method can be very accurate (often to four significant digits), but it is limited by two factors. First, it is not possible to get the current through the galvanometer to be exactly zero. Second, there are always uncertainties in
,
, and
, which contribute to the uncertainty in
.
Identify other factors that might limit the accuracy of null measurements. Would the use of a digital device that is more sensitive than a galvanometer improve the accuracy of null measurements?
One factor would be resistance in the wires and connections in a null measurement. These are impossible to make zero, and they can change over time. Another factor would be temperature variations in resistance, which can be reduced but not completely eliminated by choice of material. Digital devices sensitive to smaller currents than analog devices do improve the accuracy of null measurements because they allow you to get the current closer to zero.
If a potentiometer is used to measure cell emfs on the order of a few volts, why is it most accurate for the standard
to be the same order of magnitude and the resistances to be in the range of a few ohms?
Calculate the
of a dry cell for which a potentiometer is balanced when
, while an alkaline standard cell with an emf of 1.600 V requires
to balance the potentiometer.
(a) What is the unknown
in a potentiometer that balances when
is
, and balances when
is
for a standard 3.000-V emf? (b) The same
is placed in the same potentiometer, which now balances when
is
for a standard emf of 3.100 V. At what resistance
will the potentiometer balance?