1	Chapter 4 Ohm’s Law, Power, and Energy
2	Ohm’s Law Current in a resistive circuit Directly proportional to its applied voltage Inversely proportional to its resistance
3	Ohm’s Law For a fixed resistance Doubling voltage doubles the current For a fixed voltage Doubling resistance halves the current
4	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
5	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
6	Ohm’s Law in Graphical Form Slope (m) determined by resistor conductance
7	Ohm’s Law in Graphical Form
8	Open Circuits Current can only exist where there is a conductive path Open circuit When there is no conductive path
9	Open Circuits If I = 0 Ohm’s Law gives R = E/I = E/0 ® infinity An open circuit has infinite resistance
10	Voltage Symbols Voltage sources Uppercase E Voltage drops Uppercase V V = IR IR drops
11	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
12	Voltage Polarities
13	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
14	Current Direction If the current is in the opposite direction (going into the positive terminal), it will be absorbing power (like a resistor)
15	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
16	Current Direction
17	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
18	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
19	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
20	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
21	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:
22	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
23	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
24	Energy Energy = Power × time Units are joules Watt-seconds Watt-hours or kilowatt-hours
25	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
26	Energy Cost = Energy × cost per unit or Cost = Power × time × cost per unit
27	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
28	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
29	Law of Conservation of Energy Energy conversions Some energy may be dissipated as heat, giving lower efficiency
30	Efficiency Poor efficiency in energy transfers results in wasted energy An inefficient piece of equipment generates more heat Heat must be removed
31	Efficiency Efficiency (in %) is represented by η (Greek letter eta) Ratio of power out to power Heat removal requires fans and heat sinks
32	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%
33	Efficiency To find the total efficiency of a system Obtain product of individual efficiencies of all subsystems: h_Total = h₁ × h₂ × h₃× ∙∙∙