ECE201 Lect-2 1

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

Dr. Holbert

January 23, 2006

ECE201 Lect-2 2

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 ()

ECE201 Lect-2 3

Ohm’s Law

• v(t) = i(t) R - or - V = I R

• p(t) = i2(t) R = v2(t)/R [+ (absorbing)]

The Rest of

the Circuit

R v(t)

i(t)+

–

ECE201 Lect-2 4

Example: a 25W Bulb

• If the voltage across a 25W bulb is 120V, what is its resistance?

R = V2/P = (120V)2/25W = 576 • What is the current flowing through the

25W bulb?

I = V/R = 120V/576 = 0.208 A

ECE201 Lect-2 5

Thought Question

• When I measured the resistance of a 25W bulb, I got a value of about 40. 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 6

Open Circuit

• What if R=?

• i(t) = v(t)/R = 0

The Rest of

the Circuit

v(t)

i(t)=0+

–

ECE201 Lect-2 7

Short Circuit

• What if R=0?

• v(t) = R i(t) = 0

The Rest of

the Circuit

v(t)=0

i(t)+

–

ECE201 Lect-2 8

Class Example

• Learning Extension E2.1(a)

• Learning Extension E2.2(a)

ECE201 Lect-2 9

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 10

KCL (Kirchhoff’s Current Law)

The sum of currents entering the node is zero:

Analogy: mass flow at pipe junction

i1(t)

i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

ECE201 Lect-2 11

Class Examples

• Learning Extension E2.3(b)

• Learning Extension E2.4

• Learning Extension E2.5(a)

ECE201 Lect-2 12

KVL (Kirchhoff’s Voltage Law)

• The sum of voltages around a loop is zero:

• Analogy: pressure drop thru pipe loop

0)(1

n

jj tv

v1(t)

+ +–

–

v2(t)v3(t)

+–

ECE201 Lect-2 13

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 14

Class Examples

• Learning Extension E2.6– Use two different directions

• Learning Extension E2.7

ECE201 Lect-2 15

Electrical Analogies (Physical)

Electrical Hydraulic

Junction/Node Law

KCL: Σ I = 0 Σ G = 0

Loop Law KVL: Σ V = 0 Σ Δp = 0