Capacitors

Question 1

If there is a circuit consisting of a capacitor and a cell in series, if plate A of the capacitor is connected to the positive terminal of the cell and plate B is connected to the negative terminal of the cell, what happens when the switch is closed?

Answer 1

-Electrons are removed from plate A making it positively charged
-Electrons are deposited onto plate B making it negatively charged
-Each plate has the same charge because the same number of electrons leave and are deposited
-When the capacitor is fully charged no current flows

This would not happen without the cell, which does work on the electrons

Question 2

Define capacitance:

Answer 2

C=Q/V

capacitance (F) = charge stored (C) potential difference (V)

Question 3

Define 1 Farad

Answer 3

1 farad is equal to 1 Coulomb per Volt

Question 4

Define the energy stored in the capacitor equations:

Answer 4

E=1/2QV

E=1/2CV^2

E=1/2Q^2/C

Question 5

How to find total capacitance for a series circuit?

Answer 5

1/C = 1/C1 +1/C2 + 1/C3 +…

Question 6

How to find total capacitance for a parallel circuit?

Answer 6

C = C1 +C2 +C3 + …

Question 7

What’s the capacitance of a parallel plate capacitor, if there is a vacuum between the plates?

Answer 7

C= E_0A/d

C= Capacitance (F)
E_0=Permittivity of free space (Fm^-1)
A = Surface area of one capacitor plate (m^2)
d = Separation of plates (m)

Question 8

What’s the capacitance of a parallel plate capacitor, if there is a dielectric between the plates?

Answer 8

C=E_rEA/d

C= Capacitance (F)
E_r=The relative permittivity of the dielectric with respect to the permittivity of free space (Fm^-1)
E=Permittivity of the dielectric
A = Surface area of one capacitor plate (m^2)
d = Separation of plates (m)

Question 9

Equations for charging a capacitor when in series with a resistor R:

Answer 9

I=I_0e^-t/RC
Q=Q_0(1-e^-t/RC)
V=V_0(1-e^-t/RC)
-I is the current at a time t in the series circuit, in Amps, A
-I_0 is the initial current that flows at t=0s. This can be determined using 𝐼0 = 𝑒𝑚𝑓/R
-R is the resistance of the resistor in series with the capacitor in Ohms,
-C is the capacitance of the capacitor in Farad, F
-V is the p.d. across the capacitor at a time t, in Volts, V
-V_0 is the final p.d. in Volts, V, which will always equal the emf of the supply
-Q is the charge stored in the capacitor at time, t, in Coulombs, C
-Q_0 is the final charge on the capacitor once the current is zero, in Coulombs (C)

Question 10

Equations for discharging a capacitor through a resistor R:

Answer 10

I = I_0e^-t/RC
Q = Q_e^-t/RC
V = V_0e^-t/RC
- I is the current at a time t in the series circuit, in Amps, A
-I_0 is the initial current that flows at t=0s. This can be determined using 𝐼0 = 𝑉0/R
-R is the resistance of the resistor in series with the capacitor in Ohms
- C is the capacitance of the capacitor in Farad, F
-V is the p.d. across the capacitor at a time t, in Volts, V
-V_0 is the initial p.d. in Volts, V
-Q is the charge stored in the capacitor at time, t, in Coulombs, C
Q_0 is the initial charge on the capacitor once the current is zero, in Coulombs, C

Question 11

Define the time constant:

Answer 11

The time taken for the charge, p.d. or current to reduce down to 37% of its initial value

Question 12

Equation for time constant:

Answer 12

t=RC
t= time constant (s)
R= Resistance of resistor (Ohms)
C= Capacitance (F)