3. The capacitance of two parallel conductors of length L...

3. The capacitance of two parallel conductors of length $L$ and radius $r$, separated by a distance $d$ in air, is given by $C = \frac{\pi \epsilon L}{ln[(d - r)/r]}$ , where $\epsilon$ is the permittivity of air ($\epsilon = 8.854 \times 10^{-12}$ F/m) Write a script file that accepts user input for $d$, $L$, and $r$ and create a table that computes and displays $C$. Test the file with the values $L = 1$ m, $r = 0.001$ m, and $d =$ 0.003 to 0.01 m (use linspace to create 6 values). d (m) C(F) X 10^11 0.0030 4.0130 0.0044 2.2729 0.0058 1.7733 0.0072 1.5245 0.0086 1.3715 0.0100 1.2659

Transcript

00:01 Hi, this is a question based on capacitance where we have the expression for capacitance is given by 2 pi epsilon into l divided by lan of b by a.

00:15 So, epsilon can be written as in terms of absolute permittivity and relative permittivity divided by l into lan of b by a.

00:24 Now, from the given expressions we can substitute the values it is 2 pi into 8 .854 into 10 power minus 12 into l is 0 .3048 meters into epsilon r value is the relative permittivity given as 2 .26 divided by lan of b by a is.

00:47 So, b by a can be written as so, a is the inner conductor diameter and b is the outer conductor inner diameter.

00:56 So, b by a has the value 0 .680 divided by 0 .1045.

01:03 So, by this calculation we have the capacitance as 20 .45 pico farad.

01:07 So, 1 feet l is equal to 1 feet is converted to meters that is 0 .3048 meters.

01:14 Then in part b we have the expression for capacitance 4 pi epsilon divided by 1 by a minus 1 by b where a is the outer conductor diameter and b is the inner conductor or a is the inner conductor diameter and b is the outer conductor diameter.

01:30 So, epsilon can be written as 4 pi epsilon r into epsilon r divided by 1 by a minus 1 by b.

01:38 So, substituting the values we have 4 pi into 8 .854 into 10 power minus 12 into 2 .26 divided by 1 by 2 .5 into 10 power minus 3 minus 1 divided by 4 .5 into 10 power minus 3.

01:56 So, using this expression we have the capacitance as 1 .41 pico farad.

02:03 So, in part c again we have to consider the capacitance given by epsilon s by d.

02:07 So, this can be written as epsilon r into epsilon naught into s divided by d where s is the separation between the plates and c is the capacitance...

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