Dielectric effect in a Cilindric Capacitor - Revision history

Ist165721: Text replacement - "\]" to ""

2015-05-24T18:48:01Z

Text replacement - "\]" to "</math>"

Ist165721: Text replacement - "\[" to " $"$

2015-05-24T18:46:39Z

Text replacement - "\[" to "<math>"

Ist128595 at 21:55, 24 October 2013

2013-10-24T21:55:20Z

Ist128595 at 21:50, 24 October 2013

2013-10-24T21:50:20Z

Ist165721: Agora mudei de PVC para Polystyrene

2013-03-26T09:26:41Z

Agora mudei de PVC para Polystyrene

Ist165721 at 17:39, 21 March 2013

2013-03-21T17:39:58Z

Ist165721 at 00:34, 21 March 2013

2013-03-21T00:34:45Z

Ist165721 at 16:05, 12 March 2013

2013-03-12T16:05:28Z

Ist165721: Texto inicial

2012-05-26T16:37:12Z

Texto inicial

New page

=Description of the Experiment=
[[File:condensador-fotografia.png|thumb|Figure 1: Photo of the experimental setup]]

This experiment has the purpose of determining the capacity of a variable coax cylindrical capacitor. It has two sections, a first with a PVC dielectric and a second with air, allowing the determination of the relative dielectric constant of PVC.

<div class="toccolours mw-collapsible mw-collapsed" style="width:300px">
'''Ligações'''
<div class="mw-collapsible-content">

*Video: rtsp://elabmc.ist.utl.pt/condensador.sdp
*Laboratory: Advanced in e-lab.ist.eu[http://e-lab.ist.eu]
*Control room: Condensador Cilíndrico
*Level: ****

</div>
</div>

=Experimental Apparatus=
[[File:condensador-seccao.png|thumb|Figure 2: Sectioned schematic of the capacitor, where a=12mm and b=14mm]]

The capacitor is made from a copper tube with 12mm outer diameter and 200mm length, having been outfitted with a PVC dielectric with 100mm length. This is inside a second copper tube with 14mm inner diameter that moves along the first, thus acting as the plates of a variable capacitor. This way, the area of the capacitor corresponds only to the parts where the two cylinders coincide.

This configuration corresponds to two capacitors whose total capacity is given by the shunt between this system and a fixed capacitor (initial capacity). The experiments outputs the frequency at which the RC circuit oscillates (R = $ 1.8 M \Omega $). The period of the oscillating circuit is given by $ T= \frac{RC}{1,44} $.

=Protocol=
==Determination of the relative dielectric constant==
Take two sets of experimental data, one covering the dielectric area and the other covering air. The end-points of the sweep should be chosen in a way that allows a precise determination of the slope of the graphical representation. This slope will give the relation between the capacitor and the oscillation period (each set referring to its dielectric). The ration between the two slopes will give the relative dielectric constant for PVC.

=Advanced Protocol=
==Determination of the dielectric constant of air==
Considering Gauss's law, it is possible to determine the capacity of the cylindrical capacitor, using the formula:

\[
C = 2 \times \pi \times \epsilon _0 \times \frac{L}{ ln(\frac{b}{a}) }
\]

By doing a linear regression with the data from the section of the capacitor without the dielectric (which means the air acts as the dielectric) it is possible to accurately determine the value of the capacity. From this, reversing the formula, the air's permittivity can be found (close to vacuum, i.e. $ \epsilon _0 $).

@@ Line 39: / Line 39: @@
 <math>
 C = \frac{ 2 \pi \epsilon _0 }{ ln(\frac{b}{a}) } L
-\]
+</math>
 By doing a linear regression with the data from the section of the capacitor without the dielectric (which means the air acts as the dielectric) it is possible to accurately determine the value of the capacity. From this, reversing the formula, you can find the permittivity of the air (close to vacuum, i.e. \( \epsilon _0 \)).

@@ Line 37: / Line 37: @@
 Considering Gauss's law, it is possible to determine the capacity of the cylindrical capacitor, using the formula:
-\[
+<math>
 C = \frac{ 2 \pi \epsilon _0 }{ ln(\frac{b}{a}) } L
 \]

@@ Line 2: / Line 2: @@
 [[File:condensador-fotografia.png|thumb|Figure 1: Photo of the experimental setup]]
-This purpose of this experiment  is the determination of the capacity of a variable coax cylindrical capacitor. It has two sections, a first with a Polystyrene dielectric, and a second with air, allowing the determination of the relative dielectric constant of Polystyrene.
+This purpose of this experiment  is the determination of the capacity of a variable coax cylindrical capacitor. It has two sections, a first one with a Polystyrene dielectric, and a second one with air, allowing the determination of the relative dielectric constant of Polystyrene.
@@ Line 21: / Line 21: @@
 [[File:condensador-seccao.png|thumb|Figure 2: Sectioned schematic of the capacitor, where a=12mm and b=16mm]]
-The capacitor is made of a copper tube with an outer diameter of 12mm and 200mm long (inner plate), having been outfitted with a Polystyrene dielectric to a certain length. This is enclosed in a second copper tube with an inner diameter of 16mm  (outer plate), that moves along the first, thus acting as the plates of a variable capacitor. This way, the area of the capacitor corresponds only to the parts where the two cylinders overlap.
+The capacitor is made of a 200mm long copper tube with an outer diameter of 12mm (inner plate), having been outfitted with a Polystyrene dielectric to a certain length. This is enclosed in a second copper tube with an inner diameter of 16mm  (outer plate), that moves along the first, thus acting as the plates of a variable capacitor. This way, the area of the capacitor corresponds only to the parts where the two cylinders overlap.
 Note that, because of set-up constraints, there is a "minimum" capacitor of 26mm. In other words, x=0 actually corresponds to a 26mm long cylindrical capacitor  and Polystyrene dielectric.
@@ Line 41: / Line 41: @@
 \]
-By doing a linear regression with the data from the section of the capacitor without the dielectric (which means the air acts as the dielectric) it is possible to accurately determine the value of the capacity. From this, reversing the formula, the permittivity of the air can be found (close to vacuum, i.e. \( \epsilon _0 \)).
+By doing a linear regression with the data from the section of the capacitor without the dielectric (which means the air acts as the dielectric) it is possible to accurately determine the value of the capacity. From this, reversing the formula, you can find the permittivity of the air (close to vacuum, i.e. \( \epsilon _0 \)).

@@ Line 2: / Line 2: @@
 [[File:condensador-fotografia.png|thumb|Figure 1: Photo of the experimental setup]]
-This experiment's purpose is the determination of the capacity of a variable coax cylindrical capacitor. It has two sections, a first with a Polystyrene dielectric, and a second with air, allowing the determination of the relative dielectric constant of Polystyrene.
+This purpose of this experiment  is the determination of the capacity of a variable coax cylindrical capacitor. It has two sections, a first with a Polystyrene dielectric, and a second with air, allowing the determination of the relative dielectric constant of Polystyrene.
@@ Line 21: / Line 21: @@
 [[File:condensador-seccao.png|thumb|Figure 2: Sectioned schematic of the capacitor, where a=12mm and b=16mm]]
-The capacitor is made from a copper tube with 12mm outer diameter and 200mm length (inner plate), having been outfitted with a Polystyrene dielectric to a certain length. This is enclosed in a second copper tube with 16mm inner diameter (outer plate) that moves along the first, thus acting as the plates of a variable capacitor. This way, the area of the capacitor corresponds only to the parts where the two cylinders overlap.
+The capacitor is made of a copper tube with an outer diameter of 12mm and 200mm long (inner plate), having been outfitted with a Polystyrene dielectric to a certain length. This is enclosed in a second copper tube with an inner diameter of 16mm  (outer plate), that moves along the first, thus acting as the plates of a variable capacitor. This way, the area of the capacitor corresponds only to the parts where the two cylinders overlap.
-Note that, because of set-up constraints, there is a "minimum" capacitor of 26mm. In other words, x=0 actually corresponds to a cylindrical capacitor with 26mm length and Polystyrene dielectric.
+Note that, because of set-up constraints, there is a "minimum" capacitor of 26mm. In other words, x=0 actually corresponds to a 26mm long cylindrical capacitor  and Polystyrene dielectric.
@@ Line 29: / Line 29: @@
 ==Determination of the relative dielectric constant==
-Take two sets of experimental data, one covering the Polystyrene area and the other covering air. The end-points of the sweep should be chosen in a way that allows a precise determination of the slope of the graphical representation. This slope will give the relation between the capacity and the length of the capacitor (each set referring to its corresponding dielectric). The ratio between the two slopes will give the relative dielectric constant for Polystyrene.
+Take two sets of experimental data, one covering the Polystyrene area and the other covering air. The end-points of the sweep should be chosen in a way that allows a precise determination of the slope of the graphical representation. This slope will give the relation between the capacity and the length of the capacitor (each set referring to its corresponding dielectric). The ratio between the two slopes will give the relative dielectric constant of Polystyrene.
@@ Line 41: / Line 41: @@
 \]
-By doing a linear regression with the data from the section of the capacitor without the dielectric (which means the air acts as the dielectric) it is possible to accurately determine the value of the capacity. From this, reversing the formula, the air's permittivity can be found (close to vacuum, i.e. \( \epsilon _0 \)).
+By doing a linear regression with the data from the section of the capacitor without the dielectric (which means the air acts as the dielectric) it is possible to accurately determine the value of the capacity. From this, reversing the formula, the permittivity of the air can be found (close to vacuum, i.e. \( \epsilon _0 \)).

← Older revision		Revision as of 09:26, 26 March 2013
Line 29:		Line 29:

	==Determination of the relative dielectric constant==		==Determination of the relative dielectric constant==
−	Take two sets of experimental data, one covering the Polystyrene area and the other covering air. The end-points of the sweep should be chosen in a way that allows a precise determination of the slope of the graphical representation. This slope will give the relation between the capacity and the length of the capacitor (each set referring to its corresponding dielectric). The ratio between the two slopes will give the relative dielectric constant for ~~PVC~~.	+	Take two sets of experimental data, one covering the Polystyrene area and the other covering air. The end-points of the sweep should be chosen in a way that allows a precise determination of the slope of the graphical representation. This slope will give the relation between the capacity and the length of the capacitor (each set referring to its corresponding dielectric). The ratio between the two slopes will give the relative dielectric constant for Polystyrene.

@@ Line 19: / Line 19: @@
 =Experimental Apparatus=
-[[File:condensador-seccao.png|thumb|Figure 2: Sectioned schematic of the capacitor, where a=12mm and b=14mm]]
+[[File:condensador-seccao.png|thumb|Figure 2: Sectioned schematic of the capacitor, where a=12mm and b=16mm]]
-The capacitor is made from a copper tube with 12mm outer diameter and 200mm length (inner plate), having been outfitted with a Polystyrene dielectric to a certain length. This is enclosed in a second copper tube with 14mm inner diameter (outer plate) that moves along the first, thus acting as the plates of a variable capacitor. This way, the area of the capacitor corresponds only to the parts where the two cylinders overlap.
+The capacitor is made from a copper tube with 12mm outer diameter and 200mm length (inner plate), having been outfitted with a Polystyrene dielectric to a certain length. This is enclosed in a second copper tube with 16mm inner diameter (outer plate) that moves along the first, thus acting as the plates of a variable capacitor. This way, the area of the capacitor corresponds only to the parts where the two cylinders overlap.
 Note that, because of set-up constraints, there is a "minimum" capacitor of 26mm. In other words, x=0 actually corresponds to a cylindrical capacitor with 26mm length and Polystyrene dielectric.

@@ Line 2: / Line 2: @@
 [[File:condensador-fotografia.png|thumb|Figure 1: Photo of the experimental setup]]
-This experiment has the purpose of determining the capacity of a variable coax cylindrical capacitor. It has two sections, a first with a PVC dielectric and a second with air, allowing the determination of the relative dielectric constant of PVC.
+This experiment's purpose is the determination of the capacity of a variable coax cylindrical capacitor. It has two sections, a first with a Polystyrene dielectric, and a second with air, allowing the determination of the relative dielectric constant of Polystyrene.
-<div class="toccolours mw-collapsible mw-collapsed" style="width:300px">
+<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
 '''Ligações'''
 <div class="mw-collapsible-content">
@@ Line 21: / Line 21: @@
 [[File:condensador-seccao.png|thumb|Figure 2: Sectioned schematic of the capacitor, where a=12mm and b=14mm]]
-The capacitor is made from a copper tube with 12mm outer diameter and 200mm length, having been outfitted with a PVC dielectric with 100mm length. This is inside a second copper tube with 14mm inner diameter that moves along the first, thus acting as the plates of a variable capacitor. This way, the area of the capacitor corresponds only to the parts where the two cylinders coincide.
+The capacitor is made from a copper tube with 12mm outer diameter and 200mm length (inner plate), having been outfitted with a Polystyrene dielectric to a certain length. This is enclosed in a second copper tube with 14mm inner diameter (outer plate) that moves along the first, thus acting as the plates of a variable capacitor. This way, the area of the capacitor corresponds only to the parts where the two cylinders overlap.
-This configuration corresponds to two capacitors whose total capacity is given by the shunt between this system and a fixed capacitor (initial capacity). The experiments outputs the frequency at which the RC circuit oscillates (R = \( 1.8 M \Omega \)). The period of the oscillating circuit is given by \( T= \frac{RC}{1,44} \).
+Note that, because of set-up constraints, there is a "minimum" capacitor of 26mm. In other words, x=0 actually corresponds to a cylindrical capacitor with 26mm length and Polystyrene dielectric.
 =Protocol=
 ==Determination of the relative dielectric constant==
-Take two sets of experimental data, one covering the dielectric area and the other covering air. The end-points of the sweep should be chosen in a way that allows a precise determination of the slope of the graphical representation. This slope will give the relation between the capacitor and the oscillation period (each set referring to its dielectric). The ration between the two slopes will give the relative dielectric constant for PVC.
+Take two sets of experimental data, one covering the Polystyrene area and the other covering air. The end-points of the sweep should be chosen in a way that allows a precise determination of the slope of the graphical representation. This slope will give the relation between the capacity and the length of the capacitor (each set referring to its corresponding dielectric). The ratio between the two slopes will give the relative dielectric constant for PVC.
 =Advanced Protocol=
 ==Determination of the dielectric constant of air==
 Considering Gauss's law, it is possible to determine the capacity of the cylindrical capacitor, using the formula:
 \[
-C = 2 \times \pi \times \epsilon _0 \times \frac{L}{ ln(\frac{b}{a}) }
+C = \frac{ 2 \pi \epsilon _0 }{ ln(\frac{b}{a}) } L
 \]
@@ Line 44: / Line 46: @@
 =Links=
 *[[Determinação da Constante Dieléctrica num Condensador Cilíndrico | Portuguese Version (Versão em Português)]]