Chapter 4 – Ohm’s Law, Power and Energy

Introductory Circuit AnalysisRobert L. Boylestad

4.1 - Ohm’s Law

Every conversion of energy from one form to another can be related to this equation

In electric circuits the effect we are trying to establish is the flow of charge, or current. The potential difference, or voltage between two points is the cause (“pressure”), and the opposition is the resistance encountered

Effect = CauseOpposition

Ohm’s Law

Simple analogy: Water in a hose Electrons in a copper wire are as water in a hose Consider the pressure valve as the applied voltage and

the size of the hose as the factor that determines resistance The absence of pressure in the hose, or voltage across the wire

will result in a system without motion or reaction A small diameter hose will limit the rate at which water will flow,

just as a small diameter copper wire limits the flow of electrons

Ohm’s Law

Developed in 1827 by Georg Simon Ohm For a fixed resistance, the greater the voltage (or

pressure) across a resistor, the more the current, and the more the resistance for the same voltage, the less the current

Current is proportional to the applied voltage and inversely proportional to the resistance

Ohm’s Law

I = E/R

Where: I = current (amperes, A)

E = voltage (volts, V)

R = resistance (ohms, )

4.2 - Plotting Ohm’s Law

Insert Fig 4.6Insert Fig 4.6

Plotting Ohm’s Law

Insert Fig 4.8Insert Fig 4.8

4.3 - Power

Power is an indication of how much work (the conversion of energy from one form to another) can be done in a specific amount of time, that is, a rate of doing work

Power

Power can be delivered or absorbed as defined by the polarity of the voltage and the direction of the current

power is being delivered by a dc source if the current flows from the positive terminal

power is being absorbed by a dc source if the current flows into the positive terminal (a battery being charged)

4.4 - Wattmeters

The wattmeter is a device used to measure the power delivered by a source

Power is a function of both current and voltage levels, so four terminals must be used

2 current terminals (usually larger terminals, to ensure a solid connection)

2 voltage terminals (sometimes 3 when there is a choice of voltage level)

4.5 - Efficiency

Efficiency () of a system is determined by the following equation:

= Po / Pi

Where: = efficiency (decimal number) Po = power output

Pi = power input

Efficiency

The basic components of a generating (voltage) system are depicted below, each component has an associated efficiency, resulting in a loss of power through each stage.

Insert Fig 4.19Insert Fig 4.19

4.6 - Energy

Energy (W) lost or gained by any system is determined by:

W = Pt

Since power is measured in watts (or joules per second) and time in seconds, the unit of energy is the wattsecond (Ws) or joule (J)

EnergyThe wattsecond, however, is too small a quantity for

most practical purposes, so the watthour (Wh) and kilowatthour (kWh), were defined, as follows:

Energy (Wh) = power (W) X time (h)

The Killowatthour meter is an instrument used for measuring the energy supplied to a residential or commercial user of electricity

Energy (kWh)=power (W) x time (h)

1000

Typical wattage ratings of some common household

itemsInsert Table 4.1Insert Table 4.1

Power coming into any facility or item must be limited to ensure that the current through the lines or electrical equipment is not above the rated value

Fuses or circuit breakers are installed where the power enters the installation

Fuses have an internal metallic conductor which begins to melt if the current exceeds the fuse rated value on the case

In recent years fuses have been replaced with circuit breakers. Circuit breakers have an electromagnet that, when the current exceeds the rated value, has sufficient strength to draw the connecting metallic link out of the circuit and open the path

4.7 - Circuit Breakers, GFCIs, and Fuses

Circuit Breakers, GFCIs, and Fuses

National Electrical Code requires that outlets in the bathroom and other sensitive areas be of the Ground Fault Current Interrupt (GFCI) variety

GFCIs are designed to trip more quickly than the standard circuit breaker

GFCI senses differences in input and output currents to the outlet, and trips if they are not the same

4.8 - Applications

Microwave ovens Most rated at 500 W to 1200 W at a frequency of

2.45 GHz Heating occurs because the water molecules in the

food vibrate at such a high frequency that the friction with neighboring molecules causes the heating effect

Most microwaves are between 50% and 60% efficient

Applications

Household wiring Most older homes, without electric heating, have a

100 A service Power is broken down into different circuits utilizing

15 A, 20 A, 30 A and 40 A protective breakers Maximum load on each breaker should not exceed 80%

of its rating (12 A of a 15 A circuit breaker)

Applications

The correct gauge of wire must be used with the right circuit breaker – #14 wire up to a 15 A breaker, #12 wire up to 20 A, #10 wire up to 30 A

Grounding is a very important part of safety The National Electric Code requires that the neutral

wire of a system be grounded to an earth-driven rod, a metalic water piping system of 10 ft or more, or a buried metal plate