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Capacitance

- The Ability to Store Charge

Common Types

Electrolytic

Tanalum

Silver Mica

Parallel Plate Capacitor

Capacitance Depends on

- Separation of the plates (d) d in m

- Plate Area (A) A in m2

- Dielectric Constant (e) e in C2/N-m2

Capacitance

Capacitance depends on the construction of the

capacitor, not on the circuit it is used in.

Alternate Form for C

Recall, VW/Q

Thus, C Q/V

Example

- What is the capacitance of a capacitor if the

charge is 0.075 C held at V 400 V - C Q/V 0.075 C/400 V
- 1.875 X 10-4 f 187.5 mf

Storage of Charge

- Charges flow from the wire to one plate of the

capacitor. The insulator (dielectric) prevents

charges from flowing to the other plate. Charge

accumulates. - The accumulated charge attracts opposite charges

on the other plate. - The second plate charge pushes opposite charges

down the other wire.

Capacitors in DC Circuits

- Capacitor in a dc circuit
- Capacitor will begin charging and current will

flow - When fully charged (Q CV), current stops
- Electric field between plates cancels the field

produced by the battery voltage

Dielectric Constant

- Many texts give e in terms of a fundamental

constant (eo) and a number that depends on the

material (K) - e Keo
- eo permittivity of free space
- 8.854 X 10-12 C2/Nm2
- K dielectric constant

Typical Values of K

Example

- Two rectangular sheets of copper foil 16 X 20 cm

are separated by a thin layer of paraffin wax 0.2

mm thick. Calculate the capacitance if the

dielectric constant for the wax is 2.4.

Combining Capacitance

- Parallel plates of the capacitors are at the

same voltage as the poles of the battery.

Voltage across AA BB E

Parallel Capacitance

Q1 C1E Q2 C2E Q3 C3E

Total Charge stored is QT Q1 Q2 Q3

QT E(C1 C2 C3) CTE CT C1 C2 C3

Series Capacitance

The same current flows through each

capacitor Current is charge/time, so Q1 Q2 Q3

QT

Series Capacitance

- Kirchhoffs Voltage Law
- E V1 V2 V3

Try it

- Adding Capacitance

Example

- Three capacitors of 2.0, 3.0, and 5.0 mf are

connected in parallel to a 12 V source. - Find the charge on each capacitor.
- Find the total charge of the combination.
- Find the total charge if the same three are

connected in series to the 12 V source.

Solution (Parallel connection)

- Q1 VC1 (12 V)(2.0X 10-6f) 24 mC
- Q2 VC2 (12 V)(3.0X 10-6f) 36 mC
- Q3 VC3 (12 V)(5.0X 10-6f) 60 mC
- QT Q1 Q2 Q3 (243660)mC
- 120 mC

Solution (part 3) Series connection

RC Circuits

We can apply Kirchhoffs Laws to this circuit

also E VC VR Q/C IR

Charge Form

- For a dc voltage flowing for a time t
- I Q/t
- E Q/C QR/t Q(1/C R/t)

Current Form

- Q It
- E Q/C IR It/C IR I(t/C R)

Time dependent forms

- Notice that RC must have units of time most

books call this t RC - Current

- Voltage

(No Transcript)

Saving Links

- Charging Circuits
- RC Circuit Applet

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