RLC Circuits Flashcards
What is the symbol, circuit symbol and unit of an inductor?
Symbol: L
Circuit symbol: like the letter m
Unit: Henry, H
What is the symbol, circuit symbol and unit of a capacitor?
Symbol: C
Circuit symbol: Parallel lines
Unit: Farad, F
What is the equation to calculate the capacitance of a capacitor?
C = Q/v
C = Capacitance Q = Charge V = Voltage
What is the equation for the current through a capacitor?
i = ∆Q/∆t
When charging a capacitor, what is the equation for the charge on the capacitor with regards to current?
q = ∫ i(t) dt + q0 q = it + q0 [for constant current]
q = charge i = current t = time q0 = initial charge on the capacitor
When charging a capacitor, what is the equation for the voltage across the capacitor with regards to current?
v = 1/C × ∫ i(t) dt + v0 v = (1/C)it + v0 [for constant current]
v = voltage C = capacitance of the capacitor i = current t = time v0 = initial voltage
When charging a capacitor, what is the equation for the voltage across the capacitor with regards to the voltage applied as a factor of time and a time constant?
v = v0( 1 - e^(-t/τ) ) v = voltage v0 = applied voltage t = time τ = time constant
When charging a capacitor, what is the equation for the voltage across the capacitor with regards to the voltage applied as a factor of time and capacitance?
v = v0( 1 - e^(-t/RC) ) v = voltage v0 = applied voltage t = time R = Resistance of the resistor in the circuit C = Capacitance
When charging a capacitor, what is the equation for the power transferred to a capacitor in a circuit when there is a constant current?
p = (1/C) × i^2 × t
When charging a capacitor, what is the equation for the energy stored?
E = 0.5CV^2
When discharging a capacitor, what is the equation for the voltage across the capacitor with respect to a time constant?
v = v0e^(-t/τ)
v = voltage v0 = initial voltage t = time τ = time constant
When discharging a capacitor, what is the equation for the voltage across the capacitor with respect to a resistor in the circuit and the capacitance of the capacitor?
v = v0e^(-t/RC)
v = voltage v0 = initial voltage t = time R = Resistance of resistor in circuit C = Capacitance of capacitor
When discharging a capacitor, what is the equation to calculate the current through a capacitor?
i = i0e^(-t/RC)
i = current i0 = initial current t = time R = Resistance of resistor in circuit C = Capacitance of capacitor
When a capacitor is fully charged what is the current through the circuit?
i0 = v0/R
What is the equation for the voltage across an inductor?
v = L di/dt
v = voltage L = Inductance i = current t = time
What is the equation to combine capacitors in parallel?
Ct = C1 + C2 + C3 + … + CN
What is the equation to combine capacitors in series?
1/Ct = 1/C1 + 1/C2 + 1/C3 + … + 1/CN
What is the equations to describe the voltage and current from an AC power source?
v = Vsin(ωt) i = Isin(ωt)
v = voltage V = Max voltage ω = Angular frequency t = time i = current I = Max current
What is the equation that can relate voltage and current from an AC power source?
V = IR
e.g. i = (V/R)sin(ωt)
What is the equation for the power from an AC power source?
p = Vsin(ωt) × Isin(ωt) p = ((V^2)/R)(1-cos(2ωt))/2
p = power V = Max voltage ω = Angular frequency t = time I = Max current R = Resistance
What is an easy way to calculate RMS for sine waves?
r.m.s = peak/√2
How is Vrms calculated for non-sinusoidal waves?
Vrms = √[(1/T)∫(v^2)(t)dt]
T = Time period (which the RMS is calculated over) v = Voltage t = time
What is the equation for the voltage across an inductor connected to an AC power source?
v = Vsin(ωt)
v = voltage V = Vmax ω = Angular frequency t = Time
What is the equation for current through an inductor connected to an AC power supply
i = 1/L ∫ v(t) dt i = (-V/ωL)cos(ωt)
i = current V = Vmax L = inductance ω = Angular frequency t = time
What is the equation for sinusoidal voltage for complex ac circuits?
v(t) = V(cos(ωt) + jsin(ωt)) v(t) = Ve^jωt
What is the equation to calculate the voltage across a single capacitor for multiple capacitors joined in series?
Vx = Vt × Ct/Cx
Where Vx is the voltage across the targeted capacitor (Cx)
Where Vt is the total voltage across all the capacitors (Ct)
What is the equation for calculating the thevenin resistance?
Rth = Voc / Isc
What is norton resistance?
This is the value of the resistor in the norton equivalent circuit.
It is equal to the thevenin resistance
How is a norton equivalent circuit converted to a thevenin equivalent circuit?
Rth = Rn Vth = InRn = InRth
How is a thevenin equivalent circuit converted to a norton equivalent circuit?
Rn = Rth In = Vth / Rth
What is the equation for calculating the current through two parallel capacitors?
I2 = I × R1/(R1+R2)
