Chapter 4

Ohm’s Law, Power,

and Energy

Ohm’s Law

Current in a resistive circuit

Directly proportional to its applied voltage

Inversely proportional to its resistance

Ohm’s Law

For a fixed resistance

Doubling voltage doubles the current

For a fixed voltage

Doubling resistance halves the current

Ohm’s Law

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

Express all quantities in base units of volts, ohms, and amps or utilize the relationship between prefixes

Ohm’s Law in Graphical Form

Linear relationship between current and voltage

y = mx

y is the current

x is the voltage

m is the slope

Ohm’s Law in Graphical Form

Slope (m) determined by resistor conductance

Ohm’s Law in Graphical Form

Open Circuits

Current can only exist where there is a conductive path

Open circuit

When there is no conductive path

Open Circuits

If I = 0

Ohm’s Law gives R = E/I = E/0 ® infinity

An open circuit has infinite resistance

Voltage Symbols

Voltage sources

Uppercase E

Voltage drops

Uppercase V

V = IR

IR drops

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

Voltage Polarities

Current Direction

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

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

Current Direction

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

Current Direction

See two representations of the same current on next slide

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

Current Direction

Power

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

Power

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

Power is related to energy

Capacity to do work

Power

Power is the rate of doing work

Power = Work/time

Power is measured in watts (W)

Work and energy measured in joules (J)

One watt =

One joule per second

Power in Electrical Systems

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

P = VI

From Ohm’s Law, we can also find that

P = I²R and P = V²/R

Power is always in watts

Power in Electrical Systems

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

For example:

Power Rating of Resistors

Resistors must be able to safely dissipate their heat without damage

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

Power Rating of Resistors

A safety margin of two times the expected power is customary

An overheated resistor

Often the symptom of a problem rather than its cause

Energy

Energy =

Power × time

Units are joules

Watt-seconds

Watt-hours or kilowatt-hours

Energy

Energy use is measured in kilowatt-hours by the power company

For multiple loads

Total energy is sum of the energy of individual loads

Energy

Cost =

Energy × cost per unit or

Cost =

Power × time × cost per unit

Energy

To find the cost of running a 2000-watt heater for 12 hours if electric energy costs $0.08 per kilowatt-hour:

Cost = 2kW × 12 hr × $0.08 Cost = $1.92

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

Law of Conservation of Energy

Energy conversions

Some energy may be dissipated as heat, giving lower efficiency

Efficiency

Poor efficiency in energy transfers results in wasted energy

An inefficient piece of equipment generates more heat

Heat must be removed

Efficiency

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

Ratio of power out to power

Heat removal requires fans and heat sinks

Efficiency

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%

Efficiency

To find the total efficiency of a system

Obtain product of individual efficiencies of all subsystems:

h_Total = h₁ × h₂ × h₃× ∙∙∙


	Current in a resistive circuit
		Directly proportional to its applied voltage
		Inversely proportional to its resistance


	For a fixed resistance
		Doubling voltage doubles the current
	For a fixed voltage
		Doubling resistance halves the current


	Also expressed as E = IR and R = E/I
	Express all quantities in base units of volts, ohms, and amps or utilize the relationship between prefixes


	Linear relationship between current and voltage
	y = mx
		y is the current
		x is the voltage
		m is the slope


	Current can only exist where there is a conductive path
	Open circuit
		When there is no conductive path


	If I = 0
		Ohm’s Law gives R = E/I = E/0 ® infinity
	An open circuit has infinite resistance


	Voltage sources
		Uppercase E
	Voltage drops
		Uppercase V
	V = IR
		IR drops


	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


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


	See two representations of the same current on next slide
	Notice that a negative current actually proceeds in a direction opposite to the current arrow


	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


	The greater the power rating of a motor, the more mechanical work it can do per second
	Power is related to energy
		Capacity to do work


	Power is the rate of doing work
		Power = Work/time
	Power is measured in watts (W)
	Work and energy measured in joules (J)
	One watt =
		One joule per second


	From V = W/Q and I = Q/t, we get
	P = VI
	From Ohm’s Law, we can also find that
	P = I²R and P = V²/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:


	Resistors must be able to safely dissipate their heat without damage
	Common power ratings of resistors are 1/8, 1/4, 1/2, 1, or 2 watts


	A safety margin of two times the expected power is customary
	An overheated resistor
		Often the symptom of a problem rather than its cause


	Energy =
		Power × time
	Units are joules
	Watt-seconds
		Watt-hours or kilowatt-hours


	Energy use is measured in kilowatt-hours by the power company
	For multiple loads
		Total energy is sum of the energy of individual loads


	Cost =
		Energy × cost per unit or
	Cost =
		Power × time × cost per unit


	To find the cost of running a 2000-watt heater for 12 hours if electric energy costs $0.08 per kilowatt-hour:
		Cost = 2kW × 12 hr × $0.08 Cost = $1.92


	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


	Poor efficiency in energy transfers results in wasted energy
	An inefficient piece of equipment generates more heat
		Heat must be removed


	Efficiency (in %) is represented by η (Greek letter eta)
		Ratio of power out to power



	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%


	To find the total efficiency of a system
		Obtain product of individual efficiencies of all subsystems:
	h_Total = h₁ × h₂ × h₃× ∙∙∙