Download Recitation #6b

Physics 212 - Spring 2000
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/100
Recitation Activity 6: Capacitance
DATE:___________
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ACTIVITY PARTNERS:
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INSTRUCTOR: ____________________
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This activity is based on the following concepts:
 A capacitor consists of two isolated conductors with equal and opposite charge +Q and -Q; the
charge on the capacitor is simply referred to as "Q";
 The charge Q is proportional to the potential difference V between the two conductors: Q = CV
where the constant C is called the capacitance;
 Capacitance is measured in units of Farads: 1 F = 1 C/V;
 Capacitance depends only on the geometry of the capacitor (shape of the conductors, distance
between them) and on the "stuff" (dielectric) you put in between the conductors;
 There are 3 principal capacitor geometries that you should become familiar with:
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The parallel plate capacitor
The cylindrical capacitor
The spherical capacitor
Suppose a capacitor has a capacitance C when the space between the conducting plates is occupied by
vacuum (or air). Then, the effect of placing a dielectric in this entire space is to increase the
capacitance by a factor . This is known as the "dielectric constant" of the dielectric material.
Capacitors are used to store energy; a capacitor C with a charge Q (or potential difference V between
the plates) stores energy U = Q2/2C = CV2/2. We may view this energy as being stored in the electric
field inside the capacitor.
Capacitors are said to be in PARALLEL when the POTENTIAL DIFFERENCE across their plates is
the SAME; the equivalent capacitance is obtained by adding all the capacitances in parallel.
Capacitors are said to be in SERIES when the CHARGE on their plates is the SAME; the reciprocal
of the equivalent capacitance is obtained by adding the RECIPROCALS of all the capacitances in
series.
Questions:
The figure shows a parallel plate capacitor with plates of area A, separated
by a distance d and charged to a potential difference V. The charges on
the plates are +Q and -Q. The space between the plates is occupied by air.
-Q
+Q
Q1. Sketch in the figure the electric field lines between the plates of the
capacitor.
Q2. For the parallel plate capacitor, what equation relates the electric field
E and the potential difference V?
Q3. For the parallel plate capacitor, what equation relates the electric field
E and the charge Q? (Remember that the plates are conductors and
that the charge Q is uniformly distributed!)
d
Q4. Write down an expression for the capacitance C in terms of the geometric parameters of the
capacitor?
Analyze the following capacitor circuit:
(Note: a wire is a conductor -- as long as charges do not move in it, all points on a wire are at the
same potential!)
A
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Capacitors A and C are 1 F each.
Capacitors B and D are 2 F each.
The battery shown has a voltage of 9 V across its terminals.
B
C
Q5. Identify groups of capacitors (if any) in the circuit that are in
PARALLEL with each other:
Q6. Identify groups of capacitors (if any) in the circuit that are in
SERIES with each other:
9V
Q7. Suppose you wanted to replace all the 4 capacitors with a SINGLE capacitor that would
have the same equivalent capacitance. Calculate the value of this single capacitor.
Q8. Calculate the charge on each of the 4 capacitors A, B, C, and D.
Now capacitor A is replaced with a 4 F capacitor.
Q9. What would be the new equivalent capacitance of the circuit?
Q10. What is the potential difference across the parallel combination A, B and combination C,
D? Hint: How much charge is stored in combination A, B and combination C, D?
Q11. Calculate the charge on each of the 4 capacitors A, B, C and D.
D