Chapter 4 Ohm’s Law, Power, and Energy

2 Ohm’s Law The current in a resistive circuit is directly proportional to its applied voltage and inversely proportional to its resistance. I = E/R For a fixed resistance, doubling the voltage doubles the current. For a fixed voltage, doubling the resistance halves the current.

3 Ohm’s Law Ohm’s Law may also be 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.

4 R = 12 x 10 1 = 120  I = V/R = 12V/120  = 0.1A

5 Ohm’s Law in Graphical Form The relationship between current and voltage is linear.

6 Open Circuits Current can only exist where there is a conductive path. When there is no conductive path we refer to this as an open circuit. If I = 0, then Ohm’s Law gives R = E/I = E/0  infinity An open circuit has infinite resistance.

7 Voltage Symbols For voltage sources, use uppercase E. For load voltages, use uppercase V. For AC voltages use lowercase e.g. v Since V = IR, these voltages are sometimes referred to as IR drops.

8 Voltage Polarities The polarity of voltages across resistors is of extreme importance in circuit analysis. Place the plus sign at the tail of the current arrow.

9 Current Direction We normally show current out of the plus terminal of a source. If the actual current is in the direction of its reference arrow, it will have a positive value. If the actual current is opposite to its reference arrow, it will have a negative value.

10 Current Direction The figures at right are two representations of the same current: Conventional current is employed (opposite direction to electron flow.

11 R = 6V/25mA =240 

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

13 Power Power is the rate of doing work. Power = Work/time Power is measured in watts. One watt = one joule per second

14 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 2 R and P = V 2 /R Power is always in watts, no matter which equation is used.

15 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:

16 FIG Example 4.6. P in = IV = (120V)(5A) = 600W

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

18 Energy Energy = Power × time Units are watt-seconds, watt-hours, or more commonly, kilowatt-hours. Energy use is measured in kilowatt-hours by the power company. For multiple loads, the total energy is the sum of the energy of the individual loads.

19 Energy 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

20 Law of Conservation of Energy Energy can neither be created nor destroyed, but can be converted from one form to another. Examples: Electric energy into heat Mechanical energy into electric energy In energy conversions, some energy may be dissipated as heat, giving lower efficiency.

21 Efficiency Poor efficiency in energy transfers results in wasted energy. An inefficient piece of equipment generates more heat; this heat must be removed. Heat removal requires the use of fans and heat sinks.

22 Efficiency Efficiency will always be less than 100%. Efficiencies vary greatly: power transformers may have efficiencies of 98%, while amplifiers have efficiencies below 50%. To find the total efficiency of a system:  Total =  1 ×  2 ×  3

23  =  1 x  2 = 0.9 x 0.7 = 0.63 = 63%

24 FIG Kilowatthour meters: (a) analog; (b) digital.

25 FIG Basic components of a generating system.

26 Fuses: (a) CC-TRON® (0-10 A); (b) Semitron (0-600 A); (c) subminiature surface-mount chip fuses. Fuses

27 Circuit breakers.

28 FIG Ground fault circuit interrupter (GFCI): 125 V ac, 60 Hz, 15 A outlet.