| Link |
| Module List |
| BETA : Direct Current : Capacitors 01 : Direct Current Capacitance Charge And Power : BETA Physics Homework Exercise
Description : Direct current capacitance charge and power.
Discussion : Capacitors store electric charge on either parallel or concentric plates. The voltage induces aa electric field between the plates. The stored charge is proportional to the capacitance and the voltage. the capacitance is proportional to the area of the plates, and inversely proportional to the distance between the plates. The energy stored in the capacitor is proportional to the charge and the voltage. See Figure Charge And Capacitance For A Single Capacitor
The homework exercise has 3 sets of questions with 4 questions per set.
C, Q, Ec, Ef
V, Q, C, A
V, d, er, Ec
The basic equations are :
C = eo er A / d
Q = C V
Ec = 1/2 Q V
Ef = V / d
rearranging
V = Ef d
Q = 2 Ec / V
C = Q / V
A = C d / (eo er)
V = Q / C
d = V / Ef
er = C d / (eo A)
where
eo = permitivity constant
er = dielectric constant
A = surface area of capacitor
d = plate separation distance
C = capacitance
Q = electric charge
V = voltage across capacitor
Ec = energy stored in capacitor
Ef = electric field strength
Back To Top
|
| BETA : Direct Current : Capacitors 02 : Direct Current Two Capacitors In Series : BETA Physics Homework Exercise
Description : Direct current two capacitors in series.
Discussion : Two capacitors in series both have the same charge, but split the supply voltage. The capacitance of series capacitors is calculated similarly to the resistance of parallel resistors. See Figure Charge And Capacitance For Two Capacitors In Series
The homework exercise has 3 sets of questions with 4 questions per set.
Ce, Q, Va, Vb
Vs, Ca, Cb, Ce
Vs, Va, Vb, Cb
The basic equations are :
Ce = Ca Cb / (Ca + Cb) = 1 / (1 / Ca + 1 / Cb)
Q = Ce Vs
Va = Q / Ca
Vb = Q / Cb
rearranging
Vs = Va + Vb
Vb = Vs - Va
Ca = Q / Va
Cb = Q / Vb
Ce = Q / Vs
Q = Ca Va = Cb Vb
where
Ca Cb = capacitor A and B
Ce = equivalent capacitance for Capacitors A and B combined
Q = electric charge
Vs Va Vb = supply voltage and voltage across capacitors A and B
Back To Top
|
| BETA : Direct Current : Capacitors 03 : Direct Current Two Capacitors In Parallel : BETA Physics Homework Exercise
Description : Direct current two capacitors in parallel.
Discussion : Two capacitors in parallel both have the same voltage, but split the charge. The capacitance of parallel capacitors is calculated similarly to the resistance of series resistors. See Figure Charge And Capacitance For Two Capacitors In Parallel
The homework exercise has 3 sets of questions with 4 questions per set.
Ce, Q, Qa, Qb
Qs, Ca, Cb, Ce
Vs, Qa, Qb, Cb
The basic equations are :
Ce = Ca + Cb
Qs = Ce Vs
Qa = Ca Vs
Qb = Cb Vs
rearranging
Qs = Qa + Qb
Qb = Qs - Qa
Ca = Qa / Vs
Cb = Qb / Vs
Ce = Qs / Vs
Vs = Qs / Ce = Qa / Ca = Qb / Cb
where
Ca Cb = capacitor A and B
Ce = equivalent capacitance for Capacitors A and B combined
Vs = supply voltage
Qs Qa Qb = supply (total) charge and charge on capacitors A and B
Back To Top
|
| BETA : Direct Current : Capacitors 04 : Direct Current One Capacitor In Series With Two Capacitors In Parallel : BETA Physics Homework Exercise
Description : Direct current one capacitor in series with two capacitors in parallel.
Discussion : The charge on the two parallel capacitors is equal to the charge on the single series capacitor, and the total charge. The two capacitors in parallel both have the same voltage. See Figure Charge And Capacitance One Capacitor in Series With Two Parallel Capacitors
The homework exercise has 3 sets of questions with 6 questions per set.
Ce, Qs, Va, Vb, Qb, Qc
Vs, Qc, Ca, Cb, Cc, Ce
Vs, Va, Vb, Qc, Qb, Cb
The basic equations are :
Ce = 1 / (1 / Ca + 1 / (Cb + Cc))
Qs = Ce Vs
Va = Qs / Ca
Vb = Vs - Va
Qb = Cb Vb
Qc = Cc Vb = Qs - Qb
rearranging
Vs = Va + Vb
Qs = Qa = Qb + Qc
Qb = Qs - Qc
Qc = Qs - Qb
Ca = Qs / Va
Cb = Qb / Vb
Cc = Qc / Vb (Vc = Vb)
Ce = Qs / Vs
where
Ca Cb Cc = capacitor A B and C
Ce = equivalent capacitance for Capacitors A B and C combined
Vs Va Vb = supply voltage and voltage across capacitors A and B
Qs Qb Qc = supply (total) charge and charge on capacitors B and C (Qa = Qs)
Back To Top
|
| BETA : Direct Current : Capacitors 05 : Direct Current Charging A Capacitor In Series With A Resistor : BETA Physics Homework Exercise
Description : Direct current charging a capacitor in series with a resistor.
Discussion : The voltage across a charging capacitor follows an exponential curve which asymptotes to the supply voltage. The voltage increases rapidly at first, then more slowly as it approaches the supply voltage. The time constant is equivalent to the initial slope of the voltage curve at time equals zero. When the time equals the time constant the voltage is approximately 63 percent of the supply voltage. See Figure Charging A Capacitor
The homework exercise has 3 sets of questions with 5 questions per set.
T, Vc, Vr, I, Q
Vs, Vc, C, R, I
Vr, R, C, Q, t
The basic equations are :
T = R C
Vc = Vs (1 - exp(-t / T))
Vr = Vs exp(-t / T) = Vs - Vc
I = Vr / R
Q = C Vc
rearranging
Vc = Vs - Vr
C = Q / Vc
R = T / C
C = T / R
Vs = Vr / exp(-t / T)
t = -T log(1 - vc / Vs) = -T log(vr / Vs)
where
C = capacitor
R = resistor
Vs Vc Vr = supply voltage and voltage across capacitor and resistor
Q = charge on capacitor
I = current
t = elapsed time
T = time constant
Back To Top
|
| BETA : Direct Current : Capacitors 06 : Direct Current Discharging A Capacitor In Series With A Resistor : BETA Physics Homework Exercise
Description : Direct current discharging a capacitor in series with a resistor.
Discussion : The voltage across a charging capacitor follows an exponential decay curve which asymptotes to zero. The voltage decreases rapidly at first, then more slowly as it approaches zero. The time constant is equivalent to the initial slope of the voltage curve at time equals zero. When the time equals the time constant the voltage is approximately 37 percent of the initial voltage. See Figure Discharging A Capacitor
The homework exercise has 3 sets of questions with 5 questions per set.
T, Vc, Vr, I, Q
Vo, Vc, C, R, I
Vr, R, C, Q, t
The basic equations are :
T = R C
Vc = Vo(exp(-t / T))
Vr = Vo(1 - exp(-t / T)) = Vs - Vc
I = Vr / R
Q = C Vc
rearranging
Vc = Vs - Vr
C = Q / Vc
R = T / C
C = T / R
Vs = Vc / exp(-t / T)
t = -T log(vc / Vs) = -T log(1 - vr / Vs)
where
C = capacitor
R = resistor
Vo Vc Vr = open circuit voltage and voltage across capacitor and resistor
Q = charge on capacitor
I = current
t = elapsed time
T = time constant
Back To Top
|