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Chapter 4 Ohm’s Law, Power, and Energy

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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.

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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.

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

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

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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.

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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.

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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.

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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.

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

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11 R = 6V/25mA =240

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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.

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

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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.

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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:

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16 FIG. 4.13 Example 4.6. P in = IV = (120V)(5A) = 600W

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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.

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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.

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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

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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.

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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.

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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

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

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24 FIG. 4.16 Kilowatthour meters: (a) analog; (b) digital.

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25 FIG. 4.19 Basic components of a generating system.

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

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27 Circuit breakers.

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28 FIG. 4.23 Ground fault circuit interrupter (GFCI): 125 V ac, 60 Hz, 15 A outlet.

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