Capacitors

• The time constant is the time taken after discharge for the charge to fall to 37% of its initial value
• capacitance is the charge stored per unit voltage
• energy stored in a capacitor is half of the work done by the cell so the other half is lost in the circuit
• the area under a voltage charge graph shows the work done to add charge to a capacitor
• time constant is $\frac{-1}{gradient}$of a lnQ-t graph
• time constant is the t value for 0.37Q on Q-t graph (and same for I and V)
• it will take 5 time periods (5RC) for a capacitor to discharge
• time for charge to half is 0.69RC
• current in discharge / charge = $I=$$I\sigma e^{-\frac{t}{RC}}$
• Q and V are interchangeable in charge and discharge equations
• greater area plate = greater capacitance
• closer plates (smaller gap) = greater capacitance
• a dielectric is a material made of polar molecules
• polar molecules rotate in an electric field as the positive nucleus aligns with the negative plate and the the negative electron cloud aligns with the positive plate
• permittivity is the measure of how difficult it is to generate a uniform electric field in a material
• dielectric constant is the relative permittivity
• relative permittivity is the permittivity of material / permittivity of free space
• when discharging, the charge flows from the negative plate to the positive plate so the voltage across the plates decreases. the current also decreases as the charge difference is smaller. when the plates are balanced, the voltage and current are 0.
• polar molecules align such that the edge of the material against the negative plate is positive and the edge of the material against the positive plate is negative, creating and opposing electric field. this weakens the electric field which decreases the pd across the plates and so the same charge is stored for a lower voltage = greater capacitance.
• work needs to be done to remove a dielectric from the capacitor plates as it is attracted. this work transfers to the capacitor.