Capacitors Construction and charging and discharging

What is a capacitor? Electronic component Two conducting surfaces separated by an insulating material Stores charge Uses Time delays Filters Tuned circuits Interior light in a car stays on for a while…capacitor circuit

Capacitor construction Two metal plates Separated by insulating material ‘Sandwich’ construction ‘Swiss roll’ structure Capacitance set by... Dielectric material is good at holding onto the e-filed between the plates

Defining capacitance ‘Good’ capacitors store a lot of charge… …when only a small voltage is applied Capacitance is charge stored per volt Capacitance is measured in farads F Big unit so nF, mF and F are used Simple definition of capacitance

Graphical representation Equating to the equation of a straight line Q V Gradient term is the capacitance of the capacitor Charge stored is directly proportional to the applied voltage Simple GCSE analysis of a straight line graph

Energy stored by a capacitor By general definition E=QV product of charge and voltage By graphical consideration... Q V Area is energy stored Area term is the energy stored in the capacitor

Other expressions for energy By substitution of Q=CV Alternative expressions for energy stored

Charging a capacitor Current flow Initially High Finally I Zero Exponential model Charging factors Capacitance Resistance I t At switch on the capacitor is like a wire…high current flow When fully charged it is like the biggest resistor in the world..open circuit

Discharging a capacitor Current flow Initially High Opposite to charging Finally Zero Exponential model Discharging factors Capacitance Resistance I t Discharge current flows in the opposite direction

Voltage and charge characteristics V or Q t V or Q t Expressions for V and Q can be interchanged Charging Discharging

Time constant Product of Capacitance of the capacitor being charged Resistance of the charging circuit CR Symbol  ‘Tau’ Unit seconds Units of seconds

When t equals tau during discharge At t = tau the capacitor has fallen to 37% of its original value. By a similar analysis tau can be considered to be the time taken for the capacitor to reach 63% of full charge. Reason for t at tau being 37% of full charge

Graphical determination of tau V at 37% Q at 37% Compared to initial maximum discharge V or Q t If R is known then the value of capacitance can be found

Logarithmic discharge analysis Mathematical consideration of discharge Exponential relationship Taking natural logs equates expression to ‘y=mx+c’ Gradient is -1/Tau A bit of maths gives a nice straight line…possible basis for a good investigation

Logarithmic discharge graph lnV t Gradient term is the -1/Tau Explains the previous equation

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