# 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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