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

- Dr. Holbert
- January 23, 2006

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)

Ohms Law

- v(t) i(t) R - or - V I R
- p(t) i2(t) R v2(t)/R (absorbing)

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

Thought Question

- When I measured the resistance of a 25W bulb, I

got a value of about 40W. Whats 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.

Open Circuit

- What if R??
- i(t) v(t)/R 0

Short Circuit

- What if R0?
- v(t) R i(t) 0

Class Example

- Learning Extension E2.1(a)
- Learning Extension E2.2(a)

Kirchhoffs Laws

- Kirchhoffs 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 - Kirchhoffs Voltage Law (KVL)
- sum of voltages around any loop in a circuit is

zero

KCL (Kirchhoffs Current Law)

i1(t)

i5(t)

i2(t)

i4(t)

i3(t)

- The sum of currents entering the node is zero
- Analogy mass flow at pipe junction

Class Examples

- Learning Extension E2.3(b)
- Learning Extension E2.4
- Learning Extension E2.5(a)

KVL (Kirchhoffs Voltage Law)

v2(t)

v1(t)

v3(t)

- The sum of voltages around a loop is zero
- Analogy pressure drop thru pipe loop

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

Class Examples

- Learning Extension E2.6
- Use two different directions
- Learning Extension E2.7

Electrical Analogies (Physical)

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