C' = 2pe / ln (b/a)
e = 2 x 10-11 and µ = 4p x 10-7
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| design by pms |
C' was calculated to be 75.72 pF/m
a = 0.00042 m b = 0.002208 m
Inductance and Capacitance of Cables
The inductance and capacitance of the coaxial cable are two very important characteristics. Both, normally measured in in terms of length, play an important part in the cable's impedance and the speed by which data travels. The equations below are used to find these values.
| L' = (µ/2p)
ln (b/a) C' = 2pe / ln (b/a) e = 2 x 10-11 and µ = 4p x 10-7 |
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| L' was calculated to be 3.319 x 10-7
H/m C' was calculated to be 75.72 pF/m |
Cross section of coax
cable a = 0.00042 m b = 0.002208 m |
We were also able to experimentally calculate the capacitance of the cable by connecting it to a resistor in series to for a RC circuit. This diagram is seen below.
Therefore, by measuring the RC time constant of the circuit and using our known resistor as a value, we can easily solve for the cable's capacitance.
Click to see a graph of the RC time constant.
Our experimental value for C' is 99.8 pF/m . Compared to our value calculated above, that equates to a 24% error. Admittedly, this is a very large percent error. However, we can assume a large degree of inaccuracy in measuring the different radii (a,b) in the cable. These measurements were achieved, rather crudely, using a simple vermeer caliper. It is to be noted, however, that in future calculations, we will be using the 99.8 pF/m value, as it known to be closer to the theoretical value.
Knowing C' and L', one can also calculate the impedance of the coaxial cable using the equation:
(L' / C')1/2 = Cable Impedance
Thus we calculated Zcable to be 57.7 ohms. This is very close to our previously calculated value of 55.4 ohms. Compared to the known value of 53.5 ohms, this has a percent error of 7.8%. Super!
Knowing C' and L', one can also calculate the speed of an electrical pulse in the coaxial cable using the equation:
1/ (L' * C')1/2 = Pulse Speed
Using this equation, we calculated the pulse speed to be 1.73 x 108 m/s. Using this value to calculate c (see part 1), we get a value of 2.6 x 108 m/s. This is a percent error of 13.3 %.
Introduction | Cable Info | Lab Procedure and Results | Conclusions