6B.3 Capacitor mathematics

Question 1

what is the formula of Q using the graph while discharging a capacitor

Answer 1

Q = Q0e^-t/RC Q0 is initial rate

Question 2

as the charge in a capacitor drops while discharging the voltage would

Answer 2

drop aswell

Question 3

what is the exponential decay equation of Voltage in discharging capacitors

Answer 3

V = V0e^-t/RC

Question 4

what is the exponential decay equation of current in discharging capacitors

Answer 4

I = I0e^-t/RC

Question 5

what is the calculus proof of the exponential decay equations

Answer 5

page 51

Question 6

if t is equal to the Time constant in a exponential decay equation what will happen

Answer 6

of t=T then e^-t/RC would equal e^-1 since RC and t are the same value, and e^-1 is 0.37 so we can say when t=T the value of the charge/voltage/current drops to half its value

Question 7

what does the 37% half-life show

Answer 7

it shows that the time constant describes the decay of the charge/voltage/current on a discharging the capacitor the same was as half-life describes nuclear decay

Question 8

how can we a spreadsheet investigate the time constant and find the different outcomes of a circuit

Answer 8

we can use a spreadsheet to model a timing circuit, what we can do is input in the needed value (power supply, capacitance, discharging
resistance) and then input an equation into the spreadsheet then calculate the current different times (I = I0e^-t/RC). this helps us find the outcome of the circuit before building it, and the effects of the time constant