EEGR2111 L5

Resistive Circuits (Chap. 3)
  • Now: more complicated circuits
  • Multiple resistors and sources, i.e.:
  • So: we need to address these possibilities
  • Kirchoff voltage law and Kirchoff current law
  • Determine currents and voltages in circuits in combination with Ohm's law

    • Circuit topology
  • The interconnection of the circuit
  • Node: junction of connection between elements
  • Closed path (loop): a path through the circuit elements that passes at most once through any node and returns to the starting node.
  • How many nodes and loops in the above circuit?

    • Kirchoff's Current Law
  • The ALGEBRAIC sum of currents into a node = 0
  • True for any instant of time
  • Method: currents directed into node are positive
  • Algebraic implies including polarity as labeled
  • Below, i1 - i2 + i3 = 0:
  • Repeat for currents OUT of node. Explain.
  • Basically:
    Charge doesnt leave wires
    Charge doesnt accumulate ("bunch-up") in wires

    • Kirchoff's Voltage Law
  • The ALGEBRAIC sum of voltages around a loop = 0
  • True for any instant of time
  • Algebraic implies including polarity as labeled
  • Method: follow the voltage sign of the first terminal encountered while traversing the loop
  • Below, VR1 + VR2 + V2 -V1 = 0:
  • Repeat, following loop in opposite direction. Explain.

    • Example L5-1
  • In the above, let R1=5, R2=1, V1=1, V2= -3
  • How many nodes? loops?
  • What is KCL at the node between the two resistors?
  • Write KVL for the loop
  • Use Ohms law to substitute for the resistor voltages
  • Can we solve for i ? If so what is i ?
  • What is VR1? What is VR2 ?
  • What is the power absorbed by each of the 4 elements?
  • What is the sum of the power absorbed by each of the 4 elements?

    • Voltage divider
  • The basic voltage divider circuit is:
  • By KCL at each node: same current through the single loop
  • By KVL: VR1 + VR2 - V = 0
  • By Ohms law: VR1 = i R1, VR2 = i R2
  • So: V = i (R1 + R2 )
  • (What is i for the circuit?)
  • Finally:
    VR2 / V = ( i R2) / i (R1 + R2) = R2 / (R1 + R2)
  • What is the maximum voltage gain (VR2/VR1) ?
  • What is the maximum power gain ?

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