Capacitors Flashcards
Define and describe a capacitor
- A device designed to store charge.
- It consists of 2 conductors insulated from each other.
- When a capacitor is connected to a battery, one of the two conductors gains electrons from the battery and the other conductor loses electrons to the battery. Each plate gains an equal and opposite charge
Describe the circuit symbol for a capacitor
Two parallel lines of the same length next to each other
What is meant when it is said that the charge stored by a capacitor is Q?
One conductor stores charge +Q and the other conductor stores charge -Q
Describe a circuit to measure the charge of a capacitor at a constant current
A variable resistor, a switch, a microammeter and a cell in series with a capacitor with a voltmeter connected across the capacitor
Give the equation to calculate the charge of a capacitor being charged at a constant current at time t
Q = It
Describe the relationship between the charge of the capacitor charged at a constant current and the pd of the source that is charging it
The charge Q is proportional to the pd V
The charge stored per volt is constant
Define capacitance and give its units
The charge stored per unit pd
C = Q / V
Units: Farad (F) = 1 Coulomb per volt
Explain why energy is stored in a capacitor as it is being charged
- When the capacitor is being charged, energy is stored in it because electrons are forced onto one of its plates and taken off the other plate.
- The energy is stored in the capacitor as electrical potential energy
Give the equation for the energy stored by a capacitor
Energy stored, E = ½QV
What happens to the energy supplied by a battery to charge a capacitor of capacitance C
50% of the energy supplied by the battery (=½QV) is stored in the capacitor. The other 50% is wasted due to the resistance in the circuit as it is transferred to the surroundings when the charge flows in the current
Describe the circuit to measure the energy stored in a charged capacitor
By connecting a cell (with a voltmeter across it) to a capacitor in series with a switch. A joulemeter and light bulb are in parallel to the capacitor. The switch is arranged so that when one way, the capacitor charges from the cell, and when the other way, the capacitor discharges to the bulb
How would you measure the energy stored in a charged capacitor? (do not describe the circuit)
The capacitor pd (V) is measured and the joulemeter reading recorded before the discharge starts. When the capacitor has discharged, the joulemeter reading is recorded again.
The difference of the 2 joulemeter readings is the energy transferred from the capacitor during the discharge process.
What is a joulemeter used for?
It is used to measure the energy transfer from a charged capacitor to a light bulb when the capacitor discharges
Explain how a thundercloud acts as a parallel charged plate
Because the thundercloud is charged, a strong electric field exists between the thundercloud and the ground.
Give the potential difference between a charged thundercloud and the ground
V = Ed
where E is the electric field strength and d is the height of the thundercloud above the ground.
Give the equation for the energy stored for a thundercloud carrying a constant charge Q
Energy stored = ½QV = ½QEd
since V = Ed
Give the equation for the new amount of energy stored when a thundercloud is moved to a new height d’
Energy stored = ½QEd’
For a thundercloud moved from height d, to a new height d’, give the equation for the increase in energy stored
Increase in Energy stored = ½QEd’ - ½QEd = ½QEΔd
where Δd = d’ - d
Why is there an increase in energy stored when wind forces a thundercloud to a move further away from the ground?
The increase in energy stored is because work is done by the force of the wind to overcome the electrical attraction between the thundercloud and the ground and make the charged thundercloud move away from the ground
Why does the current decrease gradually for the discharge of a capacitor through a fixed resistor?
Because the pd across the capacitor decreases as it loses charge
Because the resistor is connected directly to the capacitor, the resistor current (=V/R) decreases as the pd decreases
Describe the shape of the graph of charge vs. time for the discharging of a capacitor through a fixed resistor
The charge decreases exponentially over time
Give the equation for the change in charge for the discharge of a capacitor through a fixed resistor
Q = Q₀e⁻ᵗ/ᶜᴿ
Give the equation for the change in potential difference for the discharge of a capacitor through a fixed resistor
V = V₀e⁻ᵗ/ᶜᴿ
Derive the equation for the change in current for the discharge of a capacitor through a fixed resistor with resistance R
I₀ = V₀ / R I = (V₀/R)e⁻ᵗ/ᶜᴿ I = I₀e⁻ᵗ/ᶜᴿ
Give the equation for the time taken for the initial charge to drop to a half its original value (the half-life)
t(½) = CRln2
Define the time constant of a CR discharge circuit
The time taken for the charge on the capacitor to fall to 37% of its initial value
τ = CR
Define the time constant of a CR charge circuit
The time take for the charge on the capacitor to reach 63% of its final charge
τ = CR
Give 2 uses of a capacitor
1) Converting AC into DC
2) Time delay circuits
Explain how a capacitor can be used with some other components to convert AC to DC
A diode allows the current from an AC supply to move in one direction only. This makes the current direct but ‘bumpy’ since it still has peaks where the positive current moves from the AC supply, and flat lines at 0A when current moves in a negative direction from the AC supply.
The capacitor charges as the current passes through the diode, and discharges as no current passes through the diode, which ‘smooths’ out the current round the circuit
Give the equation for the change in current over time for the charging of a capacitor through a fixed resistor
Q = Qₓ(1 - e⁻ᵗ/ᶜᴿ)
where Qₓ is the final charge of the capacitor
Qₓ = Cε
Give the equation for the change in pd over time for the charging of a capacitor through a fixed resistor
V = Vₓ(1 - e⁻ᵗ/ᶜᴿ)
where Vₓ is the final pd of the capacitor
but Vₓ =ε
Therefore:
V = ε(1 - e⁻ᵗ/ᶜᴿ)
Give the equation for the change in current over time for the charging of a capacitor through a fixed resistor
I = (ε / R)(1 - e⁻ᵗ/ᶜᴿ)
Describe the relationship between the change in pd and charge vs. time with the change in current vs. time for the charging of a capacitor
The charge Q, and potential difference V across the capacitor both rise exponentially whilst the current flow I, falls as an exponential function
