Reactive components

Question 1

Capacitor - V&I relationship

Answer 1

• energy storing element
• passive element
  i(t) = C dv/dt

Question 2

capacitor in DC

Answer 2

there is no change in voltage

ic(t) = 0 is an open circuit

Question 3

capacitor in AC

Answer 3

constantly changing voltage

Question 4

Inductor V&I relationship

Answer 4

• passive energy storing element
  v(t) = L di/dt
• analysis of capacitance and inductance only occurs when current or voltage is changing (dv or di)

Question 5

Capacitor and Inductor in series and parallel circuits

Answer 5

series :
1/C = 1/C1 + 1/C2
L = L1 + L2

parallel:
C = C1 + C2
1/L = 1/L1 + 1/L2

Question 6

Inductor in DC

Answer 6

VL(t) = 0

in DC, inductor is a short circuit

Question 7

First order circuit response

Answer 7

• contain a single storage element
• the circuit’s response to a changing input will first go through a transition period and will eventually settle into steady-state values.

Question 8

time constant

Answer 8

t = RC or L/R

the time constant in seconds tells you how fast the circuit will respond to change.

Question 9

first order DE + solution

Answer 9

dx(t)/dt + (1/tau)x(t) = A

general solution:
x(t) = K1 + K2* e^(-t/tau)

K1 and K2 are found using boundary conditions: value of V / I before and after change in the circuit

e.g. V(0) and V(infinity)

Question 10

Zero input response

Answer 10

STEP DOWN RESPONSE
- starts with a non-zero initial value of V/I
- has final zero value
- drops the input to zero

Question 11

Zero state response

Answer 11

STEP UP RESPONSE
- starts with a zero initial value of V/I
- has final non-zero value
- raises the input to a non-zero value

Question 12

Complete response

Answer 12

When there is a non-zero initial state and non-zero final state

complete response = zero input response + zero state response

Vc(t) = Vo*e^(-st) + (1 - e^(-st)