RLC Circuits

Question 1

What is the symbol, circuit symbol and unit of an inductor?

Answer 1

Symbol: L
Circuit symbol: like the letter m
Unit: Henry, H

Question 2

What is the symbol, circuit symbol and unit of a capacitor?

Answer 2

Symbol: C
Circuit symbol: Parallel lines
Unit: Farad, F

Question 3

What is the equation to calculate the capacitance of a capacitor?

Answer 3

C = Q/v

C = Capacitance
Q = Charge
V = Voltage

Question 4

What is the equation for the current through a capacitor?

Answer 4

i = ∆Q/∆t

Question 5

When charging a capacitor, what is the equation for the charge on the capacitor with regards to current?

Answer 5

q = ∫ i(t) dt + q0
q = it + q0 [for constant current]

q = charge
i = current
t = time
q0 = initial charge on the capacitor

Question 6

When charging a capacitor, what is the equation for the voltage across the capacitor with regards to current?

Answer 6

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

Question 7

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?

Answer 7

v = v0( 1 - e^(-t/τ) )
v = voltage
v0 = applied voltage
t = time
τ = time constant

Question 8

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?

Answer 8

v = v0( 1 - e^(-t/RC) )
v = voltage
v0 = applied voltage
t = time
R = Resistance of the resistor in the circuit
C = Capacitance

Question 9

When charging a capacitor, what is the equation for the power transferred to a capacitor in a circuit when there is a constant current?

Answer 9

p = (1/C) × i^2 × t

Question 10

When charging a capacitor, what is the equation for the energy stored?

Answer 10

E = 0.5CV^2

Question 11

When discharging a capacitor, what is the equation for the voltage across the capacitor with respect to a time constant?

Answer 11

v = v0e^(-t/τ)

v = voltage
v0 = initial voltage
t = time
τ = time constant

Question 12

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?

Answer 12

v = v0e^(-t/RC)

v = voltage
v0 = initial voltage
t = time
R = Resistance of resistor in circuit
C = Capacitance of capacitor

Question 13

When discharging a capacitor, what is the equation to calculate the current through a capacitor?

Answer 13

i = i0e^(-t/RC)

i = current
i0 = initial current
t = time
R = Resistance of resistor in circuit
C = Capacitance of capacitor

Question 14

When a capacitor is fully charged what is the current through the circuit?

Answer 14

i0 = v0/R

Question 15

What is the equation for the voltage across an inductor?

Answer 15

v = L di/dt

v = voltage
L = Inductance
i = current
t = time

Question 16

What is the equation to combine capacitors in parallel?

Answer 16

Ct = C1 + C2 + C3 + … + CN

Question 17

What is the equation to combine capacitors in series?

Answer 17

1/Ct = 1/C1 + 1/C2 + 1/C3 + … + 1/CN

Question 18

What is the equations to describe the voltage and current from an AC power source?

Answer 18

v = Vsin(ωt)
i = Isin(ωt)

v = voltage
V = Max voltage
ω = Angular frequency
t = time
i = current
I = Max current

Question 19

What is the equation that can relate voltage and current from an AC power source?

Answer 19

V = IR

e.g. i = (V/R)sin(ωt)

Question 20

What is the equation for the power from an AC power source?

Answer 20

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

Question 21

What is an easy way to calculate RMS for sine waves?

Answer 21

r.m.s = peak/√2

Question 22

How is Vrms calculated for non-sinusoidal waves?

Answer 22

Vrms = √[(1/T)∫(v^2)(t)dt]

T = Time period (which the RMS is calculated over)
v = Voltage
t = time

Question 23

What is the equation for the voltage across an inductor connected to an AC power source?

Answer 23

v = Vsin(ωt)

v = voltage
V = Vmax
ω = Angular frequency
t = Time

Question 24

What is the equation for current through an inductor connected to an AC power supply

Answer 24

i = 1/L ∫ v(t) dt
i = (-V/ωL)cos(ωt)

i = current
V = Vmax
L = inductance
ω = Angular frequency
t = time

Question 25

What is the equation for sinusoidal voltage for complex ac circuits?

Answer 25

``` v(t) = V(cos(ωt) + jsin(ωt)) v(t) = Ve^jωt ```

Question 26

What is the equation to calculate the voltage across a single capacitor for multiple capacitors joined in series?

Answer 26

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)

Question 27

What is the equation for calculating the thevenin resistance?

Answer 27

Rth = Voc / Isc

Question 28

What is norton resistance?

Answer 28

This is the value of the resistor in the norton equivalent circuit. It is equal to the thevenin resistance

Question 29

How is a norton equivalent circuit converted to a thevenin equivalent circuit?

Answer 29

``` Rth = Rn Vth = InRn = InRth ```

Question 30

How is a thevenin equivalent circuit converted to a norton equivalent circuit?

Answer 30

``` Rn = Rth In = Vth / Rth ```

Question 31

What is the equation for calculating the current through two parallel capacitors?

Answer 31

I2 = I × R1/(R1+R2)