capacitance Flashcards
(13 cards)
define capacitance
charge stored per unit potential
what are 2 forms of capacitor
- parallel plates
2.isolated spherical conductor
equation for capacitance
C = Q/V
C=capacitance (F — farad)
Q=charge
V=voltage
what the Q in capacitance equation
the charge stored on the plate/surface of capacitor, not within it
equation potential on an isolated spherical conductor
V = Q / (4πε0r)
r=radius of sphere
ε0=permittivity of free space
derive sum of capacitance equation in series
1/Ctotal = 1/C1 +1/C2+1/C3 ……..
prove:
1. capacitors in series => Vtotal=V1+V2, Q same (since current the same)
2. V=Q/C => Q/Ctotal = Q/C1 + Q/C2
=> equation proved
derive sum of capacitance equation in parallel
Ctotal = C1 + C2 + …..
prove:
1. parallel => V constant; Qtotal = Q1 + Q2 + …. (due to current)
2. Q=CV => VCtotal = VC1 + VC2 ….
proven
why is there change of electric potential when charging a capacitor
- capacitor charge by pushing electrons onto one plate and transfer electrons away from one plate to create a positive place and a negative plate
2.moving electron requires work to be done - more negative the plate alr is, more work to push electrons onto it
what does potential-charge graph look like
- positively linear
- gradient = C^-1
- area under = electric potential energy stored in the capacitor, which is same as work done to charge the capacitor
equation electrical potential energy stored in a capacitor
W = 1/2 * Q *V = 1/2 * C * V^2
how does I, V, Q charge with time when capacitor discharges
exponential decay
equation time constant when discharging a capacitor by a resistor
τ = R*C
τ=time constant; s
R=resistance
C=capacitance;F
discharging equation
X = X0 * e^(-t/RC)
X=final I, V or Q
X0=initial
e=ln constant
t=time
RC=resistance*capacitance
