Chapter 04 Ohm’s Law, Power, and Energy C-C Tsai Source: Circuit Analysis: Theory and Practice Delmar Cengage Learning Ohm’s Law (published in 1827) Current in a resistive circuit Directly proportional to its applied voltage Inversely proportional to its resistance I E R Express all quantities in base units of volts, ohms, and amps Also expressed as E = IR and R = E /I C-C Tsai 2 1 Fixed Resistance for Ohm’s Law Doubling voltage doubles the current E I R 3 C-C Tsai Fixed Voltage for Ohm’s Law Doubling resistance halves the current E I R C-C Tsai 4 4 2 Examples for Ohm’s Law Example 1 R=? 5 C-C Tsai Examples for Ohm’s Law Example 2 C-C Tsai 6 3 Examples for Ohm’s Law Example 3 Show the current direction for each circuit 7 C-C Tsai 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 C-C Tsai 8 4 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 ∞ 9 C-C Tsai Voltage Symbols Voltage source by E Voltage drop at a load by V V = IR , voltages often referred to as IR drops C-C Tsai 10 5 Example: V1 = ? V2 = ? 11 C-C Tsai 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 C-C Tsai 12 6 Examples: Voltage Polarities 13 C-C Tsai Examples: V=? V=? V=? V=? C-C Tsai 14 7 Examples: V=? V=? V=? V=? 15 C-C Tsai 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 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 C-C Tsai 16 8 Current Direction Notice that a negative current actually proceeds in a direction opposite to the current arrow 17 C-C Tsai How to light LEDs 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. R E C-C Tsai 18 9 Power Power is the rate of doing work Power = Work / time P =W / t Power is measured in watts (W) Work and energy measured in joules (J) Power is related to energy One watt = One joule per second 1W=1J/s 1 hp = 746 watts 19 C-C Tsai 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 The greater the power rating of a motor, the more mechanical work it can do per second C-C Tsai 20 10 Power Conversion for Applications 21 C-C Tsai 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 = 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: P I R C-C Tsai V PR 22 11 Examples: Power in Electrical Systems Example 1 P=? Example 2 P1 = ? and P2 = ? C-C Tsai 23 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 C-C Tsai 24 12 Power Direction Convention C-C Tsai 25 Power Direction Convention for Electric Vehicles C-C Tsai 26 13 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 27 C-C Tsai Watthour Meter Energy use is measured by watthour meter in kilowatthours (kWh), by the power company Electromechanical devices Motor with speed proportional to the load Electronic meters perform function electronically C-C Tsai Display results on digital readouts 28 14 Energy in Cost Cost = Energy × cost per unit or Cost = Power × time × cost per unit For example: Find the cost of running a 2000-watt heater for 12 hours if electric energy costs $3 per kilowatthour: Energy = 2000W × 12 h = 24kWh Cost = $3/kWh × 24kWh = $ 72 29 C-C Tsai 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 C-C Tsai 30 15 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) Pout 100% Pin 31 C-C Tsai 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% C-C Tsai 32 16 Total Efficiency To find the total efficiency of a system Obtain product of individual efficiencies of all subsystems: Total = 1 × 2 × 3 × ∙∙∙ 33 C-C Tsai Example: Total Efficiency Total =? C-C Tsai 34 17 Nonlinear and Dynamic Resistances Linear: R =V / I 35 C-C Tsai Computer Analysis Multism C-C Tsai 36 18 Computer Analysis PSpice 37 C-C Tsai Computer Analysis PSpice to measure the current C-C Tsai 38 19 Plotting Ohm’s Law With fixed resistance, the current is linear to the voltage 39 C-C Tsai 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. C-C Tsai 40 20 Problem 12 If E=28V, what does the meter indicate? 41 C-C Tsai Problem Solve the current I of the loop C-C Tsai 42 21 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 C-C Tsai 43 22