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Chapter 04

Ohm’s Law, Power, and Energy

Source: Circuit Analysis: Theory and Practice Delmar Cengage Learning C-C Tsai 2

Ohm’s Law (published in 1827)

Current in a resistive circuit

Directly proportional to its applied voltage

Inversely proportional to its resistance

Express all quantities in base units of volts, ohms, and amps

Also expressed as E = IR and R = E /I

R

EI

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Fixed Resistance for Ohm’s Law

Doubling voltage doubles the current

R

EI

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Fixed Voltage for Ohm’s Law

Doubling resistance halves the current

R

EI

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Examples for Ohm’s Law

R = ?

Example 1

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Examples for Ohm’s Law

Example 2

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Examples for Ohm’s Law

Show the current direction for each circuit

Example 3

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Ohm’s Law in Graphical Form

Linear relationship between current and voltage

y = mx versus I = E / R = G E , where G = 1/R y is the current

x is the voltage

m is the slope

Slope (m) determined by resistance or conductance

R = E / I

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Open Circuits Current can only exist where there is a

conductive path

Open circuit: Occurs when there is no conductive path

An open circuit has infinite resistance ∞

If I = 0, Ohm’s Law gives

R = E /I = E / 0 infinity ∞

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Voltage Symbols

Voltage source by E

Voltage drop at a load by V

V = IR , voltages often referred to as IR drops

Voltage source

Voltage drop or IR drop

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Example:

V1 = ?

V2 = ?

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Voltage Polarities

Polarity of voltage drops across resistors is important in circuit analysis

Drop is + to – in the direction of conventional current

To show this, place plus sign at the tail of current arrow

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Examples: Voltage Polarities

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Examples:

V = ?

V = ? V = ?

V = ?

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Examples:

V = ? V = ? V = ? V = ?

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Current Direction

Current usually proceeds out of the positive terminal of a voltage source E

If the current is actually in this direction, it will be supplying power to the circuit

If the current is in the opposite direction (going into the positive terminal), it will be absorbing power (like a resistor)

Notice that a negative current actually proceeds in a direction opposite to the current arrow

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Notice that a negative current actually proceeds in a direction opposite to the current arrow

Current Direction

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In forward direction, LED on, 10~20mA, 1.7V

In reverse direction, LED off.

For example:

If E = 6V, determine R for lighting the LED.

If E =19V, determine R for lighting the LED.

How to light LEDs

E

R

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Power

Power is the rate of doing work

Power = Work / time

P = W / t or W = P t

Power (P) is measured in watts (W)

Work (W) and energy measured in joules (J)

Power is related to energy

One watt = One joule per second

1 W = 1 J / s 1 hp = 746 watts

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Power Applications

For example: The greater the power rating of a light, the

more light energy it can produce each second

The greater the power rating of a heater, the more heat energy it can produce each second

The greater the power rating of a motor, the more mechanical work it can do per second

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Power Conversion for Applications

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Power in Electrical Systems

From V = W /Q and I = Q / t, we get

P = V I (I = V/R )

From Ohm’s Law, we can also find that

P = I 2R and P = V 2/R

Power is always in watts

We should be able to use any of the power equations to solve for V, I, or R if P is given

For example:

PRV

R

PI

R = ?

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Examples: Power in Electrical Systems

Example 2 Example 1

P = ? P1 = ? and P2 = ?

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Power Rating of Resistors

Resistors must be able to safely dissipate their heat without damage

Common power ratings of resistors are 1/8W, 1/4W, 1/2W, 1W, or 2W

Customary safety margin: two times the expected power

An overheated resistor

Often the symptom of a problem rather than its cause

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Power Direction Convention

supplying power absorbing power

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Power Direction Convention for Electric Vehicles

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Energy

Energy = Power × time

W = P ×t

Units are joules, Watt-seconds, Watt-hours or kilowatt-hours (kWh)

For multiple loads

Total energy is sum of the energy of individual loads

經濟部105.3.15召開電價費率審議委員會敲定電價調降，每度(kWh)電價平均從2.8181元降為2. 5488 元，平均每度電調降0.2693元。若以住宅用電每月平均用電330度估算，家戶可月省約89元。

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Watthour Meter

Energy use is measured by watthour meter in kilowatt-hours (kWh), by the power company

Electromechanical devices

Motor with speed proportional to the load

Electronic meters perform function electronically

Display results on digital readouts

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Energy in Cost

Cost = Energy (W) × cost per unit

or

Cost = Power (P) × time (t) × cost per unit

For example:

Find the cost of running a 2000-watt heater for 12 hours if electric energy costs $3 per kilowatt-hour(kWh):

Solution:

Energy = 2000W × 12 h = 24kWh

Cost = $3/kWh × 24kWh = $ 72 C-C Tsai 30

Law of Conservation of Energy

Energy can neither be created nor destroyed

Converted from one form to another

Examples:

Electric energy into heat

Mechanical energy into electric energy

Energy conversions

Some energy may be dissipated as heat, giving lower efficiency

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Efficiency

Poor efficiency in energy transfers results in wasted energy

An inefficient piece of equipment generates more heat

Efficiency (in %) is represented by η (Greek letter eta)

%100

P

P

in

out

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Efficiency

Heat removal requires fans and heat sinks

Always less than (or equal to) 100%

Efficiencies vary greatly:

Power transformers may have efficiencies of up to 98%

Some amplifiers have efficiencies below 50%

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Total Efficiency

To find the total efficiency of a system

Obtain product of individual efficiencies of all subsystems:

Total = 1 × 2 × 3 × ∙∙∙

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Example: Total Efficiency

Total =?

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Nonlinear and Dynamic Resistances

Linear: R =V / I

Nonlinear: R ≠V / I

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Computer Analysis

Multism

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Kernel abilities

1. What is Ohm’s law? Please give an example.

2. How to light a LED? Please give an example.

3. How to calculate the dissipated power on a resistor? Please give an example.

4. How to estimate the power fee per month for a family? Please give an example.

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Problem 12

If E=28V, what does the meter indicate?

E=28V

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Another Problem

Solve the current I of the loop

I = ?

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An Energy Problem

Given electric products that used per day as below, what cost a family pay per month? (NT$2.5 is for a kWh) 100W-Lamp 6 hours 300W-TV 5 hours

500W-Refrigenator 10 hours