Capacitors Flashcards
What is capacitance?
Capacitance is the charge stored per unit potential difference in a capacitor.
C = Q/V given in exam
What is a capacitor?
A capacitor is an electrical component that stores charge.
A parallel-plate capacitor is made of two parallel conducting plates with an insulator between them (A.K.A a dielectric).
What is permittivity?
Permittivity is a measure of how difficult it is to generate an electric field in a certain material.
What is relative permittvity?
Relative permittivity is the ratio of the permittivity of a material to the permittivity of free space:
εr = ε1/ε0 not given in exam
Relative permittivity is also called the dielectric constant.
How does using dielectrics increase capacitance?
- Dielectric made up of lots of polar molecules - positive end and negative end
- Initially, molecules are pointing in a bunch of random directions
- After charge is applied, negative ends are attracted to positive plate and vice versa - they become aligned
- Each molecule has its own electric field, which in new alignment opposes original electric field
- Reduces overall electric field, which reduces potential difference needed to charge capacitor - so capacitance increases
C = Q/V
What does the time taken to charge or discharge a capacitor depend on?
The time taken to charge or discharge a capacitor depends on:
- The capacitance of the capacitor - affects the amount of charge that can be transferred at a given potential difference
- The resistance of the circuit - affects the current in the circuit
What is the equation for the potential difference of a charging capacitor?
Equation for potential difference of a charging capacitor:
V = V0(1 - e^(-t/RC))
Same as charge for charging capacitor:
Q = Q0(1 - e^(-t/RC))
What is the equation for the current of a charging capacitor?
Equation for the current of a charging capacitor:
I = I0e^(-t/RC)
Same as all discharging equations.
Is the exponential graph for current against time for a charging capacitor positive or negative?
Current against time for a charging capacitor:
Negative
Is the exponential graph for potential difference against time for a charging capacitor positive or negative?
Potential difference against time for a charging capacitor:
Positive
Is the exponential graph for charge against time for a charging capacitor positive or negative?
Charge against time for a charging capacitor:
Positive
Is the exponential graph for current against time for a discharging capacitor positive or negative?
Current against time for a discharging capacitor:
Negative
Is the exponential graph for potential difference against time for a discharging capacitor positive or negative?
Potential difference against time for a discharging capacitor:
Negative
Is the exponential graph for charge against time for a discharging capacitor positive or negative?
Charge against time for a discharging capacitor:
Negative
What is the time constant, τ?
Time constant is product of resistance and capacitance.
τ = RC
1/e = 0.37
Time taken for the charge, potential difference or current of a discharging capacitor to fall to 37% of fully charged value.
(1 - 1/e) = 0.63
Time taken for the charge or potential difference of a charging capacitor to rise to 63% of fully charged value.
How can you find the time constant from log-linear graphs?
Q = Q0e^(-t/RC)
ln(Q) = (-1/RC)t + ln(Q0)
Plot ln(Q) against time t, you get a straight line.
Gradient of graph is (-1/RC) and y-intercept is ln(Q0).
What is the time to halve charge, current or potential difference of a discharging capacitor?
Time to halve charge, current or potential difference of a discharging capacitor:
T1/2 = 0.69RC
E.g. Find time taken for charge to halve.
Q = 1/2Q0 1/2Q0 = Q0e^(-t/RC) 1/2 = e(-t/RC) ln(1/2) = ln(e(-t/RC)) ln(1) - ln(2) = (-t/RC) t = 0.69RC
