Capacitors

Question 1

Define Capacitance

Answer 1

Charge stored per unit Volt [F]

Question 2

What do the gradient and area under this graph represent?

Answer 2

Gradient → Capacitance

Area → Work done (Energy Stored)

Question 3

What is wrong with this?

Answer 3

C = capacitance → not the charge!!!

Question 4

When building a capacitor how do you maximize the capacitance?

Answer 4

1. Increase the area of the plates
2. Decrease the plate separation
3. Place dielectric between plates

Question 5

What does it mean if the relative permittivity of a dielectric (ε_r) is 5.0?

Answer 5

The capacitor stores 5x more charge with the dielectric between the plates!

Question 6

How does adding a dielectric increase the capacitance of a capacitor?

Answer 6

1. Dielectric contains polarised molecules
2. They align with the field between the plates
3. Bigger negative charge attracts more electrons onto negative plate
4. Repels more electrons away from positive plate
5. V same but Q has increased

Question 7

What happens if the dielectric is removed?

(Capacitor still connected to battery)

Answer 7

1. Polarised molecules removed
2. Some electrons leave negative plate
3. Attracts more electrons to positive plate
4. Q has decreased but V same
5. C decreases (C=Q/V)

Question 8

What happens if the dielectric is removed?

(When the Capacitor is disconnected from battery)

Answer 8

1. Polarised molecules removed
2. But charge is trapped on plates
3. Same Q but with lower C
4. V increases (V=Q/C)

Question 9

How does this capacitor charge?

(When switch 1 is closed)

Answer 9

1. Electrons flow from the negative terminal of the battery
2. To the connected parallel plate (right plate)
3. Electrons are repelled from the opposite plate (left)
4. And attracted to the positive terminal of the battery
5. Charge across Parallel plates

Question 10

How does this capacitor discharge?

(When switch 2 is closed)

Answer 10

1. Electrons flow from the negative plate (right)
2. Through the resistor
3. To the other plate (left)
4. Decreasing charge difference across plates

Question 11

Define time constant

Answer 11

Time constant is how long it takes for a capacitor to…

1. Charge to 63% of max charge (0.63Q₀)
2. Discharge 63% of Q₀ (down to 0.37Q₀)

Question 12

What factors affect the time constant of a circuit?

Answer 12

1. The resistance of the components in the circuit (Capacitor R=0)
2. Capacitance of the capacitor

Question 13

Complete this discharging curve for a capacitor

Answer 13

Question 14

Complete this discharging curve for a capacitor

Answer 14

Question 15

Complete this discharging curve for a capacitor

Answer 15

Question 16

Complete this charging curve for a capacitor

Answer 16

Question 17

Complete this charging curve for a capacitor

Answer 17

Question 18

Complete this charging curve for a capacitor

Answer 18

Question 19

How do you read off the time constant from this graph?

Answer 19

Read off time when charge (or current or voltage) has decreased to 37% initial

Question 20

How do you read off the time constant from this graph?

Answer 20

Read off time when charge (or current or voltage) has increased to 63% final

Question 21

Explain why the I-t graph is exponential when a capacitor discharges

Answer 21

1. Potential difference across capacitor drives large current through resistor
2. Charge across plates decreases
3. Potential difference across the plates decreases
4. Current gets smaller and smaller

Question 22

Explain why the I-t graph is exponential when a capacitor charges

Answer 22

1. Battery drives current round circuit
2. Charge build up on capacitor plates
3. Potential difference builds up across plates
4. Difference in PD between battery and capacitor gets less
5. So smaller push on electrons
6. Smaller current

Question 23

What is wrong here?

Answer 23

80% is the decrease in charge (∆Q)

So it discharges to 20% of initial Q=0.2Q₀

Question 24

How do you make a capacitor charge/discharge at a constant rate?

Answer 24

Use a variable resistor

Decreasing resistance

To keep charging/discharging current constant

Question 25

How do the graphs change if a **capacitor is charging at a constant rate**?

Answer 25

Current → Constant Voltage and Charge → Linear

Question 26

How do the graphs change if a **capacitor is discharging at a constant rate**?

Answer 26

Current → Constant Voltage and Charge → Linear

Question 27

How do you **show Q=0.37Q₀ after 1 time constant?**

Answer 27

**Set t=RC**

Question 28

What is wrong here?

Answer 28

Capacitor is **discharging at a constant rate** So **current is constant** **Can't use Q=Q₀e^-t/RC equations**

Question 29

How does the potential difference of the **resistor change as the capacitor charges**?

Answer 29

**NOTE: V_R+V_C=V₀**

Question 30

How does the potential difference of the **resistor change as the capacitor discharges**?

Answer 30

**NOTE: V_R+V_C=V₀**

Question 31

For a **discharging capacitor,** what does the **gradient of the Q-t** graph give?

Answer 31

**Current** at that instant

Question 32

For a **charging capacitor,** what does the **gradient of the Q-t** graph give?

Answer 32

**Current** at that instant

Question 33

For a **discharging capacitor,** what does the **area of the I-t** graph give?

Answer 33

**Charge lost** in that region

Question 34

For a **charging capacitor,** what does the **area of the I-t** graph give?

Answer 34

**Charge gained** in that region

Question 35

Define **half life of a capacitor**

Answer 35

Time constant is how long it takes for a capacitor to… 1. **Charge to 50%** of max charge (0.50Q₀) 2. **Discharge 50%** of Q₀ (down to 0.50Q₀)

Question 36

How is a Capacitor's **half life** calculated?

Answer 36