4 - capacitor

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Last updated 12:32 PM on 6/4/26
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15 Terms

1
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give the formula for capacitance across plates

C = q/V [F]

2
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calculate E of plate capacitor

choose Gaussian cylinder with top touching (+) plate and bottom in air

=> flux through upper surface = 0

=> flux through side = 0 (E is parallel)

=> flux through lower surface = “formula“

*σ is charge per WHOLE area A

*a is cylinder area

*dA points down - always take from inside to outside

<p>choose Gaussian cylinder with top touching (+) plate and bottom in air</p><p>=&gt; flux through upper surface = 0</p><p>=&gt; flux through side = 0 (<strong>E</strong> is parallel)</p><p>=&gt; flux through lower surface = “formula“</p><p>*σ is charge per WHOLE area A</p><p>*a is cylinder area</p><p>*d<strong>A</strong> points down - always take from inside to outside</p>
3
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calculate V and hence C of plate capacitor

V = - qd / ε0 A

C = ε0 A/d => smaller distance between plates makes larger capacitance

<p>V = - qd / ε<sub>0</sub> A</p><p>C = ε<sub>0</sub> A/d =&gt; smaller distance between plates makes larger capacitance</p>
4
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calculate E hence V hence C for cylindrical capacitor

=> E of straight wire from Gauss where L is wire length and R is wire radius

<p>=&gt; <strong>E</strong> of straight wire from Gauss where L is wire length and R is wire radius</p><p></p>
5
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what is q and what is V for capacitors in parallel - what is the total capacitance then

q1 and q2 but V is SAME

C = C1 + C2

6
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what is q and what is V for capacitors in series - what is the total capacitance then

V1 and V2 but q is SAME

1/C = 1/C1 + 1/C2

7
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what is current between two capacitors in series

I = 0: In DC circuit, when the capacitors are fully charged, they act like an open circuit. Because no more charge moves through the system, the current drops to zero

8
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how does work play into capacitors

capacitors store energy = work done to get net charge on the two plates

9
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give the total work to charge capacitor from 0 to q

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10
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what is energy density given total work to charge a capacitor from 0 to q

w ~ E2

w = [J/m3]

<p>w ~ E<sup>2</sup> </p><p>w = [J/m<sup>3</sup>]</p>
11
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define dielectric

an insulator that transfer an electric field without electric conduction

12
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what happens when put a dielectric in an E field?

E induces a macroscopic dipole

polarisation: the molecules align with each side taking a polarity while whole remains neutral

13
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what happens to the electric field when there is a dielectric?

dielectric reduces the E field in the capacitor by εr : when polarisation occurs, it makes its own field Ei that opposes the initial Eo

<p>dielectric reduces the <strong>E</strong> field in the capacitor by ε<sub>r</sub> : when polarisation occurs, it makes its own field E<sub>i</sub> that opposes the initial E<sub>o</sub> </p>
14
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what happens to the capacitance when there is a dielectric?

C becomes εr times larger since C= q/V = q / Ed

15
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define dielectric field strangth

max field strength without dielectric breaking down = becoming a conductor