Ohm's Law (2.1); Kirchhoff's Laws (2.2) by oxp14855

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									  Ohm's Law (2.1);
Kirchhoff's Laws (2.2)

       Dr. Holbert
    January 23, 2006


        ECE201 Lect-2    1
                 Resistors
• A resistor is a circuit element that dissipates
  electrical energy (usually as heat)
• Real-world devices that are modeled by
  resistors: incandescent light bulbs, heating
  elements (stoves, heaters, etc.), long wires
• Resistance is measured in Ohms (W)


                    ECE201 Lect-2               2
                 Ohm’s Law
• v(t) = i(t) R - or -                   V=IR
• p(t) = i2(t) R = v2(t)/R               [+ (absorbing)]

                                 i(t)
                The                       +
               Rest of              R         v(t)
                the
               Circuit                    –


                         ECE201 Lect-2                     3
       Example: a 25W Bulb
• If the voltage across a 25W bulb is 120V,
  what is its resistance?
      R = V2/P = (120V)2/25W = 576 W
• What is the current flowing through the
  25W bulb?
      I = V/R = 120V/576 W = 0.208 A


                   ECE201 Lect-2              4
           Thought Question
• When I measured the resistance of a 25W
  bulb, I got a value of about 40W. What’s
  wrong here?
• Answer: The resistance of a wire increases
  as the temperature increases. For tungsten,
  the temperature coefficient of resistivity is
  4.5x10-3/oK. A light bulb operates at about
  5000oF.
                    ECE201 Lect-2                 5
               Open Circuit
• What if R=?
                                      i(t)=0
                          The                  +
                         Rest of                   v(t)
                          the
                         Circuit               –


• i(t) = v(t)/R = 0


                      ECE201 Lect-2                       6
               Short Circuit
• What if R=0?
                                      i(t)
                        The                  +
                       Rest of               v(t)=0
                        the
                       Circuit               –


• v(t) = R i(t) = 0


                      ECE201 Lect-2                   7
            Class Example
• Learning Extension E2.1(a)
• Learning Extension E2.2(a)




                  ECE201 Lect-2   8
           Kirchhoff’s Laws
• Kirchhoff’s Current Law (KCL)
  – sum of all currents entering a node is zero
  – sum of currents entering node is equal to
    sum of currents leaving node
• Kirchhoff’s Voltage Law (KVL)
  – sum of voltages around any loop in a
    circuit is zero
                    ECE201 Lect-2             9
KCL (Kirchhoff’s Current Law)
                        i1(t)     i5(t)
                i2(t)                   i4(t)

                            i3(t)

The sum of currents entering the node is zero:
                    n

                   i (t )  0
                   j 1
                            j


     Analogy: mass flow at pipe junction
                        ECE201 Lect-2           10
           Class Examples
• Learning Extension E2.3(b)
• Learning Extension E2.4
• Learning Extension E2.5(a)




                  ECE201 Lect-2   11
KVL (Kirchhoff’s Voltage Law)
               +           –
                   v2(t)                   +
           +
   v1(t)                                       v3(t)
           –
                                           –


• The sum of voltages around a loop is zero:
                    n

                   v
                   j 1
                            j   (t )  0

• Analogy: pressure drop thru pipe loop
                        ECE201 Lect-2                  12
              KVL Polarity
• A loop is any closed path through a circuit
  in which no node is encountered more than
  once
• Voltage Polarity Convention
  – A voltage encountered + to - is positive
  – A voltage encountered - to + is negative



                     ECE201 Lect-2              13
             Class Examples
• Learning Extension E2.6
  – Use two different directions
• Learning Extension E2.7




                     ECE201 Lect-2   14
 Electrical Analogies (Physical)
               Electrical        Hydraulic
Junction/Node KCL: Σ I = 0       ΣG=0
Law
Loop Law      KVL: Σ V = 0       Σ Δp = 0




                 ECE201 Lect-2               15

								
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