Charging

• Capacitors are charged by a?power supply?(eg. a battery)
• When charging, the electrons are pulled from the plate connected to the positive terminal of the power supply
  • Hence the plate nearest the positive terminal is?positively charged
• They travel around the circuit and are pushed onto the plate connected to the negative terminal
  • Hence the plate nearest the negative terminal is?negatively charged
• As the negative charge builds up, fewer electrons are pushed onto the plate due to electrostatic repulsion from the electrons already on the plate
• When no more electrons can be pushed onto the negative plate, the charging stops

A parallel plate capacitor is made up of two conductive plates with opposite charges building up on each plate

• At the start of charging, the current is large and gradually falls to zero as the electrons stop flowing through the circuit
  • The current decreases?exponentially
  • This means the rate at which the current decreases is proportional to the amount of current it has left
• Since an equal but opposite charge builds up on each plate, the potential difference between the plates slowly increases until it is the same as that of the power supply
• Similarly, the charge of the plates slowly increases until it is at its maximum charge defined by the?capacitance?of the capacitor

Graphs of variation of current, p.d and charge with time for a capacitor charging through a battery

• The key features of the charging graphs are:
  • The shapes of the p.d. and charge against time graphs are identical
  • The current against time graph is an?exponential decay?curve
  • The initial value of the current starts on the y axis and decreases exponentially
  • The initial value of the p.d and charge starts at 0 up to a maximum value

Discharging

• Capacitors are?discharged?through a resistor with?no?power supply present
• The electrons now flow back from the negative plate to the positive plate until there are equal numbers on each plate and no potential difference between them
• Charging and discharging is commonly achieved by moving a switch that connects the capacitor between a power supply and a resistor

The capacitor charges when connected to terminal P and discharges when connected to terminal Q

• At the start of discharge, the current is?large?(but in the opposite direction to when it was charging) and gradually falls to zero
• As a capacitor discharges, the current, p.d and charge all decrease?exponentially
  • This means the rate at which the current, p.d or charge decreases is proportional to the amount of current, p.d or charge it has left
• The graphs of the variation with time of current, p.d and charge are all identical and follow a pattern of?exponential decay

Graphs of variation of current, p.d and charge with time for a capacitor discharging through a resistor

• The key features of the discharge graphs are:
  • The shape of the current, p.d. and charge against time graphs are identical
  • Each graph shows exponential decay curves with decreasing gradient
  • The initial values (typically called?I0,?V0?and?Q0?respectively) start on the y axis and decrease exponentially
• The rate at which a capacitor discharges depends on the?resistance?of the circuit
  • If the resistance is?high, the current will decrease and charge will flow from the capacitor plates more slowly, meaning the capacitor will take longer to discharge
  • If the resistance is?low, the current will increase and charge will flow from the capacitor plates quickly, meaning the capacitor will discharge faster

Properties of Capacitor Discharge Graphs

• From electricity, the charge is defined:

ΔQ?=?IΔt

• Where:
  • I?= current (A)
  • ΔQ?= change in charge (C)
  • Δt?= change in time (s)
• This means that the?area?under a current-time graph for a charging (or discharging) capacitor is the?charge?stored?for a certain time interval

The area under the I-t graph is the total charge stored in the capacitor in the time interval Δt

• Rearranging for the current:

• This means that the?gradient?of the?charge-time graph is the?current?at that time

The gradient of a discharging and charging Q-t graph is the current

• In the?discharging?graph, this is the?discharging?current at that time
• In the?charging?graph, this is the?charging?current at that time
• To calculate the gradient of a curve, draw a tangent at that point and calculate the gradient of that tangent

Step 1: Draw a tangent at?t?= 4

Step 2: Calculate the gradient of the tangent to find the current?I