AH 2.2.1 Capacitors

Question 1

In the circuit below the capacitor is initially uncharged.

The switch is moved to position 1.

a) what happens to the capacitor?
b) sketch the current v time graph for this situation.
c) sketch the voltage v time graph for this situation

Answer 1

a) The capacitor charges
b) & c) See the graphs below.

Question 2

In the circuit below the capacitor is initially charged.

The switch is moved to position 2.

a) what happens to the capacitor?
b) sketch the current v time graph for this situation.
c) sketch the voltage v time graph for this situation.
d) Explain the sign of the current in the current discharge graph.

Answer 2

a) The capacitor discharges.
b) & c) See the graphs below which show both the charging and DISCHARGING of the capacitor.

Question 3

a) Define the time constant τ in an RC circuit (a circuit containing a resistor R in series with a capacitror C).
b) State the equation for the time constant in an RC circuit and sate the unit of τ.

Answer 3

a)

τ = the time for the charge (or voltage) to increase to 63% of its initial value.

= the time for the charge (or voltage) to decay to 37% of its initial value.

b) τ = RC

τ has the unit of seconds

Question 4

Insert the missing words below.

In an RC circuit, an uncharged capacitor can be considered to be fully charged after a time approximately equal to ………..

In an RC circuit, a fully charged capacitor can be considered to be fully discharged after a time approximately equal to ………….

Answer 4

In an RC circuit, an uncharged capacitor can be considered to be fully charged after a time approximately equal to 5τ.

In an RC circuit, a fully charged capacitor can be considered to be fully discharged after a time approximately equal to 5τ

Where τ = the time constant for the RC circuit

Question 5

The graphs below show the graphs of current in an RC circuit.

a) In the left-hand graph is the capacitor charging or discharging?
b) In the right -hand graph is the capacitor charging or discharging?

The graphs show the effect of changing the values of resistance R or capacitance C.

c) Copy the graphs and replace the letters D, E, F & G with the either ‘resistor’ or ‘capacitor’

Answer 5

a) Charging
b) Charging
c) See the graphs below.

Question 6

The circuit below may be used het investigate the way current behaves in a A.C. capacitive circuit.

a) AC current I is directly proportional to three different variables

What are they?

b) State the equation which relates I to these variables

Answer 6

a) I is directly prportional to

• the supply voltage V_s
• the AC supply frequency f
• the capacitance itself C

b) I = 2πfVC

Question 7

​Look at the circuit below which shows a capacitor with an AC supply.

Assuming the capacitance C is contant and the supply Voltage V is constant, sketch a graph to show the variation of current I with frequency f for a capacitive circuit.

Answer 7

Question 8

a) State the equation for capacitive reactance in terms of voltage and current in an AC circuit.
b) Develop the equation to include frequency

Answer 8

a) X_c = V/I
b) X_c = V/I

= V / 2πfCV

X_c = 1 / 2πfC V cancels

Question 9

State as many uses of capacitors as you can.

Answer 9

1. Timing circuits (e.g. in a pelican crossing)
2. High-pass electronic filter (e.g. cross-over network in loudspeaker)
3. Flashing neon light circuit.
4. Smoothing circuits (smoothing rectified AC)
5. Radio receiver circuit
6. Camera flash units
7. Capitive touch screens

Question 10

Look at the circuit below. The switch is now closed.

a) Sketch the charging graph of current v time
b) Calculate the current at switch-on and indicate this on your graph
c) Sketch the graph of voltage v time for the capacitor
d) Indicate the maximum voltage across the capacitor on your V-t graph
e) Add to your voltage graph a line indicating the voltage across the resistor
f) Calculate the charge stored on the capacitor.
g) If it takes 0.6 s for the capacitor to fully charge, find the average charging current

Answer 10