Capacitance Define capacitance and its unit.

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1 Capacitance Define capacitance and its unit.
Solve problems about capacitance. Demonstrate charge-discharge of a capacitor. Discuss the factors which affect the capacitance of a parallel plate capacitor. HL: Demonstrate parallel plate capacitors factors. HL: Solve problems about parallel plate capacitors. HL: Solve problems about energy stored in a capacitor. Know and demonstrate that capacitors conduct AC but not DC. Give some uses of capacitors.

2 Define Capacitance As the charge on a conductor increases, its electrical potential increases as well. The capacitance of a conductor is the ratio of the charge on the conductor to its potential. Formula: 𝐶= 𝑄 𝑉 The unit of capacitance is the farad (F). 1 farad = 1 coulomb per volt. The farad is very big, so we tend to see microfarads (1 𝜇𝐹 = 10 −6 𝐹), nanofarads (1 𝑛𝐹= 10 −9 𝐹), or picofarads (1 𝑝𝐹 = 10 −12 𝐹).

3 Solve Problems e.g. A conductor has a potential of 6 V when a charge of 6 𝜇C is placed on it. What is its capacitance? e.g. The capacitance of a conducting sphere is 20 pF. If its potential is 5000 V, find the charge on it. What is the positive charge stored on a 5 μF capacitor when connected to 120 V d.c. supply?

4 Charge and Discharge a Capacitor
Also demonstrates energy stored in a capacitor Charge and Discharge a Capacitor Connect a power supply to a capacitor (charging). Remove the power supply and replace it with a bulb. Note that the bulb will light for a moment, then go dim as the capacitor discharges. This shows that energy was stored in the capacitor.

5 Discuss Parallel Plate Capacitors
A parallel place capacitor consists of two parallel conductive plates separated by an insulating region called a dielectric. When charged, the plates store equal and opposite amounts of charge.

6 Discuss Parallel Plate Capacitance
Capacitance, C of a parallel plate capacitor is: proportional to cross-sectional area of the plates (∝𝐴) proportional to permittivity of the medium between them (∝𝜀) inversely proportional to the distance between them (∝ 1 𝑑 ) Altogether, the formula becomes: 𝐶= 𝜀𝐴 𝑑

7 HL: Solve Problems e.g. The area of overlap of the parallel plates in an air- spaced capacitor is 20 cm2. The distance between the plates is 1 mm. Given 𝜀 0 =8.9× 10 −12 𝐹 𝑚 −1 , find the capacitance. If the space between the plates is replaced with mica of relative permittivity 7, calculate the capacitance.

8 HL: Solve Problems The plates of an air filled parallel plate capacitor have a common area of 40 cm2 and are 1 cm apart. The capacitor is connected to a 12 V d.c. supply. Calculate the capacitance of the capacitor. Calculate the magnitude of the charge on each plate. What is the net charge on the capacitor?

9 HL: Demonstrate Parallel Plate Caps
Connect a parallel plate capacitor to a high voltage power supply. Connect one plate to ground and the other to an electroscope. Note the divergence in the electroscope’s leaves. Move the plates closer together and note the increase in the leaves’ divergence ⇒ the capacitance increases. Decrease the overlap between the plates and note the decrease in the leaves’ divergence ⇒ the capacitance decreases.

10 HL: Demonstrate Parallel Plate Caps
Place different insulating slabs between the plates. Note the decrease in the leaves’ divergence ⇒ the capacitance decreases.

11 Give Uses of Capacitors
Tuning radios. Flash guns (e.g. old camera flashes). Smoothing signals. Filtering signals.

12 HL: Solve Problems about Energy
The energy stored in a capacitor is given by: Formula: 𝑊= 1 2 𝐶 𝑉 2 W = energy, C = capacitance, V = voltage

13 HL: Solve Problems about Energy
Calculate the energy stored in a 5 𝜇F capacitor when a potential difference of 20 V is applied to it. A capacitor of capacitance 100 𝜇F is charged to a potential difference of 20 V. What is the energy stored in the capacitor? 2007 Q5f E = J Q5e E = 0.02 J

14 HL: Solve Problems about Energy
Two parallel metal plates are placed a distance 𝑑 apart in air. The plates form a parallel plate capacitor with a capacitance of 12 𝜇F. A 6 V battery is connected across the plates. Calculate the charge on each plate. Calculate the energy stored in the capacitor. 2014 Q9 i) 72 𝜇C ii) E = 216 𝜇J

15 HL: Solve Problems about Energy
A 64 𝜇F capacitor in a defibrillator is charged to a potential difference of 2500 V. The capacitor is discharged through electrodes attached to the chest of a heart attack victim. Calculate: the charge stored on each plate of the capacitor the energy stored in the capacitor the average power generated as the capacitor discharges over 10 ms. 2009 Q9 Q = 0.16 C ii) E = 200 J

16 Demonstrate that Capacitors Conduct A.C. but not D.C.
Connect a capacitor and light bulb to a d.c. power supply. Note the bulb does not light. Replace the d.c. power supply with an a.c. power supply. Note the bulb lights. Thus, capacitors conduct a.c. but not d.c.