Capacitors Flashcards
Define Capacitance
Charge stored per unit Volt [F]
What do the gradient and area under this graph represent?
Gradient → Capacitance
Area → Work done (Energy Stored)
What is wrong with this?
C = capacitance → not the charge!!!
When building a capacitor how do you maximize the capacitance?
- Increase the area of the plates
- Decrease the plate separation
- Place dielectric between plates
What does it mean if the relative permittivity of a dielectric (εr) is 5.0?
The capacitor stores 5x more charge with the dielectric between the plates!
How does adding a dielectric increase the capacitance of a capacitor?
- Dielectric contains polarised molecules
- They align with the field between the plates
- Bigger negative charge attracts more electrons onto negative plate
- Repels more electrons away from positive plate
- V same but Q has increased
What happens if the dielectric is removed?
(Capacitor still connected to battery)
- Polarised molecules removed
- Some electrons leave negative plate
- Attracts more electrons to positive plate
- Q has decreased but V same
- C decreases (C=Q/V)
What happens if the dielectric is removed?
(When the Capacitor is disconnected from battery)
- Polarised molecules removed
- But charge is trapped on plates
- Same Q but with lower C
- V increases (V=Q/C)
How does this capacitor charge?
(When switch 1 is closed)
- Electrons flow from the negative terminal of the battery
- To the connected parallel plate (right plate)
- Electrons are repelled from the opposite plate (left)
- And attracted to the positive terminal of the battery
- Charge across Parallel plates
How does this capacitor discharge?
(When switch 2 is closed)
- Electrons flow from the negative plate (right)
- Through the resistor
- To the other plate (left)
- Decreasing charge difference across plates
Define time constant
Time constant is how long it takes for a capacitor to…
- Charge to 63% of max charge (0.63Q0)
- Discharge 63% of Q0 (down to 0.37Q0)
What factors affect the time constant of a circuit?
- The resistance of the components in the circuit (Capacitor R=0)
- Capacitance of the capacitor
Complete this discharging curve for a capacitor
Complete this discharging curve for a capacitor
Complete this discharging curve for a capacitor
Complete this charging curve for a capacitor
Complete this charging curve for a capacitor
Complete this charging curve for a capacitor
How do you read off the time constant from this graph?
Read off time when charge (or current or voltage) has decreased to 37% initial
How do you read off the time constant from this graph?
Read off time when charge (or current or voltage) has increased to 63% final
Explain why the I-t graph is exponential when a capacitor discharges
- Potential difference across capacitor drives large current through resistor
- Charge across plates decreases
- Potential difference across the plates decreases
- Current gets smaller and smaller
Explain why the I-t graph is exponential when a capacitor charges
- Battery drives current round circuit
- Charge build up on capacitor plates
- Potential difference builds up across plates
- Difference in PD between battery and capacitor gets less
- So smaller push on electrons
- Smaller current
What is wrong here?
80% is the decrease in charge (∆Q)
So it discharges to 20% of initial Q=0.2Q0
How do you make a capacitor charge/discharge at a constant rate?
Use a variable resistor
Decreasing resistance
To keep charging/discharging current constant
How do the graphs change if a capacitor is charging at a constant rate?
Current → Constant
Voltage and Charge → Linear
How do the graphs change if a capacitor is discharging at a constant rate?
Current → Constant
Voltage and Charge → Linear
How do you show Q=0.37Q0 after 1 time constant?
Set t=RC
What is wrong here?
Capacitor is discharging at a constant rate
So current is constant
Can’t use Q=Q0e-t/RC equations
How does the potential difference of the resistor change as the capacitor charges?
NOTE: VR+VC=V0
How does the potential difference of the resistor change as the capacitor discharges?
NOTE: VR+VC=V0
For a discharging capacitor, what does the gradient of the Q-t graph give?
Current at that instant
For a charging capacitor, what does the gradient of the Q-t graph give?
Current at that instant
For a discharging capacitor, what does the area of the I-t graph give?
Charge lost in that region
For a charging capacitor, what does the area of the I-t graph give?
Charge gained in that region
