Chapter 4 – Ohm’s Law, Power and Energy Introductory Circuit Analysis Robert L. Boylestad 1

4.2 - Ohm’s Law Every conversion of energy from one form to another can be related to this equation. In electric circuits the effect we are trying to establish is the flow of charge, or current. The potential difference, or voltage between two points is the cause (“pressure”), and resistance is the opposition encountered. 2

Ohm’s Law Simple analogy: Water in a hose Electrons in a copper wire are analogous to water in a hose. Consider the pressure valve as the applied voltage and the size of the hose as the source of resistance. The absence of pressure in the hose, or voltage across the wire will result in a system without motion or reaction. A small diameter hose will limit the rate at which water will flow, just as a small diameter copper wire limits the flow of electrons. 3

Ohm’s Law Developed in 1827 by Georg Simon Ohm For a fixed resistance, the greater the voltage (or pressure) across a resistor, the more the current. The more the resistance for the same voltage, the less the current. Current is proportional to the applied voltage and inversely proportional to the resistance. 4

Ohm’s Law Where: I = current (amperes, A) E = voltage (volts, V) R = resistance (ohms, ) Put the eq 4.2 – 4.4 on slide, I would like to arrange them one they have been inserted so that they make sense. 5

4.3 - Plotting Ohm’s Law 6

Plotting Ohm’s Law Insert Fig 4.8 Put Fig 4.9 in and the Equations 4.5 and 4.7 7

4.4 - Power Power is an indication of how much work (the conversion of energy from one form to another) can be done in a specific amount of time; that is, a rate of doing work. 8

Power Power can be delivered or absorbed as defined by the polarity of the voltage and the direction of the current. 9

4.5 - Energy Energy (W) lost or gained by any system is determined by: W = Pt Since power is measured in watts (or joules per second) and time in seconds, the unit of energy is the wattsecond (Ws) or joule (J) 13

Energy The watt-second is too small a quantity for most practical purposes, so the watt-hour (Wh) and kilowatt-hour (kWh) are defined as follows: The killowatt-hour meter is an instrument used for measuring the energy supplied to a residential or commercial user of electricity. 14

4.6 - Efficiency Efficiency () of a system is determined by the following equation:  = Po / Pi Where:  = efficiency (decimal number) Po = power output Pi = power input 11

Efficiency The basic components of a generating (voltage) system are depicted below, each component has an associated efficiency, resulting in a loss of power through each stage. Insert Fig 4.19 12

Typical wattage ratings of some common household items Insert Table 4.1 15

4.7 - Circuit Breakers, GFCIs, and Fuses Power coming into any facility or item must be limited to ensure that the current through the lines or electrical equipment is not above the rated value. Fuses or circuit breakers are installed where the power enters the installation. Fuses have an internal metallic conductor which begins to melt if the current exceeds the fuse rated value on the case. In recent years fuses have been replaced with circuit breakers. Circuit breakers have an electromagnet that, when the current exceeds the rated value, has sufficient strength to draw the connecting metallic link out of the circuit and open the path. 16

Circuit Breakers, GFCIs, and Fuses National Electrical Code requires that outlets in the bathroom and other sensitive areas be of the Ground Fault Circuit Interrupt (GFCI) variety. GFCIs are designed to trip more quickly than the standard circuit breaker. GFCI senses differences in input and output currents to the outlet, and trips if they are not the same. 17

4.8 - Applications Microwave ovens Most microwaves are rated at 500 W to 1200 W at a frequency of 2.45 GHz. Heating occurs because the water molecules in the food vibrate at such a high frequency that the friction with neighboring molecules causes the heating effect. Most microwaves are between 50% and 60% efficient. 18

Applications Household wiring Most older homes, without electric heating, have a 100 A service. Power is broken down into different circuits utilizing 15 A, 20 A, 30 A and 40 A protective breakers. Maximum load on each breaker should not exceed 80% of its rating (12 A of a 15 A circuit breaker). 19

Applications The correct gauge of wire must be used with the right circuit breaker – #14 wire up to a 15 A breaker, #12 wire up to 20 A, #10 wire up to 30 A. Grounding is a very important part of safety. The National Electric Code requires that the neutral wire of a system be grounded to an earth-driven rod, a metallic water piping system of 10 ft or more, or a buried metal plate. 20