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WJP, PHY381 (2010)
Wabash Journal of Physics
v4.0, p.1
Precision Measurement of the Resistance of a YBCO
Superconductor
Jonathan Barlow, Lucian Lupiski, and M.J. Madsen
Department of Physics, Wabash College, Crawfordsville, IN 47933
(Dated: May 4, 2010)
We measured the resistance of a YBCO high-TC superconductor through the superconducting transition. We measured the voltage drop across the superconductor
using an AC four-wire measurement with lock-in detection, sensitive down to the
mΩ level. We measured the resistance of the sample during the superconducting
state to be 30 ± 7 µΩ, compared to the room temperature resistance of 5.79 ± 0.04
mΩ.
High-Temperature Superconductors (HTS) have exsisted since the mid-1980s when Bednorz and Muller first synthesized them in 1986[? ]. These superconductors were different
from their predecessors in that the critical temperature of superconductivity was signicantly
higher [? ] which allowed superconductors to become economically viable for large and
small scale experiments[? ]. One such HTS is Ytrium Barium Cupper Oxide (YBCO). In
1987 Wu and Chu and their respective grad students synthesized YBCO and reported that
it has a superconducting transition at 93 K, above the temperature of liquid nitrogen [? ].
These measurements of a YBCO sample used in education [? ] are merely preliminary measurements, to test our measurement procedure. The procedure we propose will be
similar to process to measure the transition temperature and maximum magnetic flux of a
superconducting wire sample (provided by SuperPower inc.) as a pre-cursor for building a
superconducting high-field electromagnet at Wabash College.
Though the resistance of a superconductor is non-ohmic, we model the superconductor
as isotropic. This constrains [? ] the current-voltage (I − V ) relationship across the sample
to be an odd function in voltage V . In order to measure the resistance a superconductor we
need to understand the relationship between the current flowing across the superconductor,
the voltage drop across it, and its resistance. The relation between current and voltage can
be expressed as [? ],
I = c1 V + c2 V 3 ....
(1)
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Wabash Journal of Physics
v4.0, p.2
Where the first term is Ohm’s Law,
V = IR
(2)
Though the resistance of the sample is non-Ohmic, we note that if the voltage drop across the
sample drops to zero, there will be no resistance, since we know that there is still a current
flowing through the superconductor. This means that as the resistance of the superconductor
drops the the voltage we measure should decrease as well. Prior work [? ] has shown a
dramatic drop in the resistance of the YBCO sample through the superconducting phase,
though their data is ambiguous as to the real resistance of their sample after the transition.
We improve on their work by making a precision measurement of the resistance after the
transition to the superconducting state.
We model our measurement as an ideal battery connected in series with a load resistor
and test resistor. A voltmeter is connected in parallel with the test resistor (as in fig. 1).
According to the Kirchoff’s law we can find the voltage drop of the battery (∆Vbatt ) to be
given by
∆Vbatt = ∆VRL + ∆V(Rtest +Rvoltmeter )
(3)
Where ∆VRL is the change in voltage across the load resistor and ∆V(Rtest +Rvoltmeter ) is the
change in voltage across the test resistor (Rtest ) and voltage resistor (Rvoltmeter ) which are
connected in parallel to the battery. The load resistor can modeled as an ohmic resistor. Also
when the resistance of the test resistor is small compared to the resistance of the voltmeter,
the current will flow almost exclusively through the test resistor. For small voltage drops, we
need only look at the first term of equation 1, Ohm’s law, to find the voltage drop across the
test resistor (∆Vtest ). Fortunately the voltages we obtained for the superconductor at room
temperature and while superconducting were fairly small (less than 100 mV ). Therefore
we believe we can report the voltages using this approximation. We can then rewrite the
previous equation solving for the current through the battery, load resistor, and test resistor
as
∆Vbatt
Rtest + RL
is kept small, we can approximate equation 4 as,
I=
Because RL is 49.8 ± .2 Ω and Rtest
I=
∆Vbatt
.
RL
(4)
(5)
Using Ohm’s law to look at the resistance of the test resistor as a function of current, I and
change in voltage across the test resistor voltage, ∆Vtest , and plugging in the result of the
WJP, PHY381 (2010)
Wabash Journal of Physics
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previous equation we find,
Rtest =
∆Vtest
RL
∆Vbatt
(6)
We use a four wire resistance measurement in order to make precision measurements for
resistances close to zero [? ]. In a four wire measurement setup current is driven through
the sample through two wires connected to a digital function generator ( Pasco PI-9587C)
and a series load resistor (RL )tolimitthetotalcurrentinthecircuitto1.64 ±.07 × 10−3 Amps
. The other two wires measure the RMS voltage drop across the superconductor sample
through the lock-in amplifier (Stanford Research Systems SR 530) which is locked to the
frequency of the source digital function generator. Figure 1 displays this setup. The lockin amplifier helps us do this by providing different measurement scales for measurements of
very low voltages. The lock-in also subtracts the noise from the data by locking to the signal
of the power source and removing frequency changes away from the reference signal [? ].
We use a frequency of 23 Hz (a prime number below the power-grid range), this minimizes
the outside interference. We also measured the root-mean-squared (RMS) voltage (Vrms )
by using a digital oscilloscope (Tektronics TDS 2012B). To do this, we measure the source
voltage drop with the oscilloscope, extract the voltage-as-a-function-of-time data and use a
sinusoidal fit to get the ∆Vrms (with uncertainty) of the output of the function generator.
Wire
2
Rtest
Wire
3
Wire
4
Wire
1
∆Vtest
Power Source
∆Vbatt
RL
FIG. 1: In our model we have a battery connected in series to a load resistor and test resistor. A
voltmeter is connected in parallel to the test resistor.
In comparison to the model, Vbatt , is Vrms of the digital function generator and I is the
Irms of the alternating current in the circuit. Also Rtest is the resistance of the HTS, RHT S .
Therefore eq. 6 becomes
RHT S =
∆VHT S
RL
∆Vrms
(7)
WJP, PHY381 (2010)
Wabash Journal of Physics
. Where the uncertainty, u(RHT S ) will be given by
s
2 2 2
u(RL )
u(∆VHT S )
u(∆Vrms )
+
+
u(RHT S ) = RHT S
RL
∆VHT S
∆Vrms
v4.0, p.4
(8)
To maintain a consistent temperature across the entire YBCO sample, we keep liquid
nitrogen from touching any one part of the HTS by containing the HTS in a flexible plastic
container (50 ± 2mL) and placing this plastic container (HTS inside) into a 600 mL pyrex
beaker. Placing this into the beaker, we add liquid nitrogen to the 500 mL line only allowing
the liquid nitrogen to drop to 450 mL. We encase the HTS in this plastic container because its
brass housing is not air-tight and liquid nitrogen seeped in in earlier trials. The thermocouple
is inside this brass housing, so when liquid nitrogen seeps in, we get incorrect data for the
temperature of the YBCO sample.
1 2
3 4
Thermocouple
Plastic Container
Beaker
Brass Housing
HTS
Foam Insulator
Liquid Nitrogen
FIG. 2: Here is a figure of our setup used to control the temperature of our HTS. The beaker is
a 600 mL Pyrex beaker. 1, 2, 3, and 4 are the wires from fig. 1. The thermocouple goes into the
brass housing as do wires 1, 2, 3, and 4. The plastic container protects the inside of the brass
housing from direct exposure to the liquid nitrogen.
We measure the voltage across the HTS as a function of time, VR(t) . The Vrms from the
digital function generator stays fairly constant we can obtain a good measurement for it
by connecting the digital function generator to an oscilloscope. For one trail we found a
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Wabash Journal of Physics
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Vrms of roughly 0.815V. At room temperature we found a VHT S of 0.95 ± 0.06 mV which by
equations 7 and 8 corrospond to an RHT S of 5.79 ± .04mΩ. And upon immersion in liquid
nitrogen we found a VHT S of 0.05 ± 0.001 mV which corresponds to an RHT S of 0.030 ± 0.007
mΩ. This is a drop by about a factor of 200. Based on previous results[? ] [? ] and
theory [? ] we would expect the resistance to drop to zero. We currently believe that the
reason that we are not recording a resistance of zero is due to contact resistance of the wires
connected to the superconductor. This data yields a transition temperature of roughly 90
K. This result agrees with the previous measurement made at this facility [? ].
0.005
Resistance (Ohm)
0.004
0.003
0.002
0.001
0
80
90
100
110
120
Temperature (K)
130
140
150
FIG. 3: This is a graph of the resistance of the YBCO superconductor as a function of temperature
as it is cooled in a bath of liquid nitrogen.
Although we have recorded a sharp drop in resistance we have yet to record the predicted resistance of zero. We would like to be able to at least drop orders of magnitude for
the superconductor while it is superconducting. Although this is non-zero even after the
superconducting transition, we expect this to be mostly due to contact resistance at the
solder points on the HTS. However we find a very small resistance, which leads us to believe
that our setup and procedure can be applied to measuring the resistance of our wire while
superconducting. After obtaining this measurement we will move forward with our ultimate
WJP, PHY381 (2010)
Wabash Journal of Physics
v4.0, p.6
goal of creating a superconducting high-field magnet.
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Physics Department, The College of Wooster , (2008)
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516-519 (2009)
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