EEGR2111 L3

Passive/active elements
  • Passive - energy absorbed from rest of circuit always non-negative
  • Active - capable of delivering energy
  • Resistors
  • Simplest circuit element
  • Passive
  • Voltage-current relationship: v = i R or i = v / R
  • R is resistance in Ohms (V/A)
  • Symbol for ohms is greek capital omega:
  • Physical property of material R = rho L / A
  • rho = resistivity Ohm-M
  • L = length, A = cross-sectional area
  • Physical layout important for integrated circuits
  • Ohms Law
  • As above: v = i R
  • Plot: straight line through origin
  • NOTE: this (v = i R) is for passive convention!!!
  • Can also be written i = v / R = v G
  • G = 1/R = conductance in siemens (will also see mho)
  • Power in resistors
  • p(t) = v(t) i(t)
  • Substitute using v = i R
  • So what is the energy from time - infinity to t?
  • Explain why this is a passive device
  • Example L3-1:
  • A 10 V battery is in series with a 10 Ohm resistor
  • What is the current?
  • What power p(t) is absorbed by the resistor?
  • What energy is delivered from t=1 to t=2 seconds.
  • Example L3-2:
  • A voltage v(t) = cos(10 t) is in series with a 10 Ohm resistor
  • What is the current?
  • What power p(t) is absorbed by the resistor?
  • What energy is delivered from t=1 to t=2 seconds.
  • Example L3-3:
  • A current i(t) = cos(10 t) runs through a 10 Ohm resistor
  • What is the voltage?
  • What power is absorbed by the resistor?
  • What energy is delivered from t=1 to t=2 seconds.
  • Example L3-4:
  • A current i(t) below runs through a 10 Ohm resistor
  • What is the voltage?
  • What power p(t) is absorbed by the resistor?
  • What energy is delivered from t=1 to t=2 seconds.

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