Sections 23-26

Question 1

What is the equation for self inductance L? What are its units? What is its circuit diagram symbol?

Answer 1

NΦ/I [Henry] It’s circuit diagram symbol is a coil.

Question 2

What is the self-induced e.m.f in an inductor? What does this mean?

Answer 2

ϵ = -L dI/dt This means there is a voltage drop across the inductor.

Question 3

What is the equation for energy input/stored in L?

Answer 3

u = 1/2 * L*I^2

Question 4

What is the equation for energy density of L?

Answer 4

u = U/V = B^2/2μ0, where u is the energy density, U is the denergy store and V is the volume of the inductor.

Question 5

What happens to inductance when inductors are in series/parallel?

Answer 5

Same relationship as resistors.

Question 6

How do transformers work?

Answer 6

Two inductors with same cross-section but different number of windings. Using Faraday’s Law, ϵs/Ns = ϵp/Np, therefore if Ns> Np, it steps the e.m.f up, and if Ns < Np it steps the voltage down.

Question 7

What is the equation relating emf and current for transformers?

Answer 7

ϵs*Is = ϵp*Ip

Question 8

How can an AC voltage be represented in complex form?

Answer 8

V = V0*e^(iωt) = V0(cos(ωt) + i*sin(ωt))

Question 9

How can you represent a phase difference in complex form?

Answer 9

V1 = V0*e^(iωt)

V2 = V0*e^(iωt + iϕ) = V1*e^iϕ = rotation by ϕ in argand diagram

Question 10

What is the equation for the voltage of a DC and AC supply?

Answer 10

-DC

V = RI

-AC

V = LI, where L is the complex impedance or the impedance.

Question 11

What is the complex impedance of a resistor? Why is this?

Answer 11

L = R

Rearrange the equation for complex voltage of a AC source and you get this.

Question 12

What is the complex impedance of a capacitor? How do you derive this?

Answer 12

L = 1/jωC

Use Q = CV and I = dQ/dt, then introduce complex form and rearrange (including cos and sin and stuff)

• V(compl) = V0e^(jωt)
• I = C dV/dt
• I(compl) = jωC*V0e^(jωt) = jωC*V(compl)
• V(compl) = LI(compl), so Lc = 1/jωC

Question 13

What is the complex impedance of an inductor? How do you derive this?

Answer 13

L = jωL

Use V = L dI/dt, and V(t) = V0 cos(ωt), and find the current I(t) by integrating.

• This gives I(t) = V0/ωL * sin(ωt)
• Since V = L dI/dt, V(compl) = jωLI(compl)
• Use V = LI and rearrange

Question 14

How do you find the true value of something if it has a complex number in it?

Answer 14

Find the magnitude of the ‘vectors’ (so j or i is squared and therefore removed)

Question 15

In capacitors and inductors, what is the phase difference between V(t) and I(t)?

Answer 15

pi/2

Question 16

How do you work out the phase of the complex impedance of an LRC circuit?

Answer 16

Write Leq = L0*e^(jϕ)

ϕ = tan^-1(IM(Leq)/RE(Leq))

Question 17

What are the three types of LRC circuits? How do you create these?

Answer 17

Low-pass filter - LRC circuit with R and C in series and Vout over the capacitor

High-pass filter - LRC circuit with R and L in series and Vout over the inductor

Notch filter - LRC circuit with R L and C in series and Vout over L and C

Question 18

How much power is dissipated in inductors and capacitors with an AC current flowing through them?

Answer 18

None.

Question 19

What is the equation for rms V and rms I?

Answer 19

Irms = I0/sqrt(2)

Vrms = V0/sqrt(2)

Question 20

What is the equation for power in an LRC circuit?

Answer 20

P = 1/2 * V0 * I0 * cos(ϕ) = Vrms * Irms * cos(ϕ)