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 • p(t) = i2(t) R = v2(t)/R
V=IR
[+ (absorbing)]
i(t)
The
Rest of
the
Circuit
+
R
v(t)
–
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
the
Circuit
+
v(t)
–
• i(t) = v(t)/R = 0
ECE201 Lect-2
6
Short Circuit
• What if R=0?
i(t)
The
Rest of
the
Circuit
+
v(t)=0
–
• 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)
+
v1(t)
+
–
v2(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
Junction/Node KCL: Σ I = 0
Law
Loop Law
KVL: Σ V = 0
ECE201 Lect-2
Hydraulic
ΣG=0
Σ Δp = 0
15