Capacitor Functions and Iterative Mapping

Question 1

How do capacitors work?

Answer 1

Capacitors store charge. They consist of electrical plates which used to be large plates, but now typically are made from foil, which act as the conductor and are separated by an insulator. When electrons move from the battery to the plate, negative charge builds on one side, and positive on the other as electrons flow to the battery. This is charge separation.

Question 2

What is capacitance and how is it represented?

Answer 2

Capacitance equation, C=Q/V where Q is charge and V is voltage. Capacitance is charge separated per volt and a Q-V graph gives capacitance as the gradient. Measured in farads, typically micro and pico.

Question 3

How does discharge work?

Answer 3

When the switch connects the capacitor to the cell, the capacitor charges. Moving it to the second position connects it to the bulb in parallel. Negative charge moves to the positive plate, discharging the capacitor as shown with the lamp glowing.

Question 4

What are formulae for energy of capacitors?

Answer 4

Energy = difference in charge * voltage for a small dQ.

E=1/2 QV Q=CV E=1/2CV^2 E=1/2 Q^2/C

Question 5

What are capacitors used for?

Answer 5

Energy storing devices such as camera flash circuits and computers.

Question 6

What does the capacitor discharge experiment show?

Answer 6

When doing a capacitor discharge experiment under timing, use smaller time intervals for smaller capacitance and resistance, and a data logger with a voltmeter.
These experiments show exponential curves for V-t as V is proportional to charge, Q-t, and I-t as I is proportional to V for constant resistance.

Question 7

What equation is derived from difference in charge = difference in time * current for the iterative formula?

Answer 7

dQ=-Idt = -V/R dt=-Q/RC dt
As resistance and capacitance are constant, the change in charge is proportional to the charge remaining.
dQ/dt=-Q/RC

Question 8

What important formulae are needed for mapping the iterative function of charge falling against time?

Answer 8

Qnew = Q - difference in Q.

Q lost = I * dt

Question 9

What exponential formulae were derived from the iterative mapping?

Answer 9

Q=Q0e^-t/RC
V=V0e^-t/RC
I=I0e^-t/RC