Equivalent Circuits

Question 1

Equivalence

Answer 1

• A property that applies between various systems.

Question 2

Why place so much importance on the electrical equivalent of other systems?

Answer 2

• Circuits ares cheap to manufacture (they are small and light).
• Circuits can be made to performs dynamic operations very cost effectively (eg, differentiation/integration).

Question 3

Mathematically and Physically equivalent systems?

Answer 3

• Same differential equation
• The derivative has a similar meaning in the power equation (coefficients in DE describe similar physical processes… eg, storage of potential energy or dissipation of energy)

Question 4

Power

Answer 4

• Difference in energy per unit time.
• Product of voltage across a component and current.

P = VI

Question 5

Power Formulae

Answer 5

POWER = GENERALIZED FORCE X GENERALIZED FLOW

> Voltage x Current (circuit)
Force x Speed (rocket)
Pressure x Flow Rate (water flow)
Torque x Angular Speed (angular/rotation)

Question 6

Virtual Power

Answer 6

• This method is used for modelling dynamic systems using these rules:
  > Along components sharing same generalized flow, we can write equilibrium equations for generalized forces… Kirchhoff’s voltage law!
  > For components sharing same generalized force, we can write generalized flow continuity equations… Kirchhoff’s current law!

Question 7

Series RLC Circuit

Answer 7

V(AC) = IR + C^-1 integral(I(AC)dt) + L(dI(AC)/dt)

Question 8

Series electrical vs Series mechanical

Answer 8

• Induction is equivalent to mass
• Resistance is equivalent to damping
• The inverse of capacitance is equivalent to stiffness.

Question 9

Parallel RLC Circuit

Answer 9

I = C(dS/dt)^2 + (1/R)(dS/dt) + (1/L)S

Question 10

Parallel electrical vs Parallel mechanical

Answer 10

• ## They are mathematically equivalent but not physically equivalent.