ELECTRICITY & MAGNETISM (Fall 2011) LECTURE # 10 BY MOEEN GHIYAS

TODAY’S LESSON (Ohm’s Law, Power & Energy – Chapter 4) (Series Circuit – Chapter 5) Introductory Circuit Analysis by Boylested (10 th Edition)

Today’s Lesson Contents Chapter 4 Energy Circuit Breakers, GFCIs and Fuses Applications Solutions to Problems Chapter 5 Introduction Series Circuit Voltage Sources in Series

Energy Power is the rate of doing work A motor may have the horsepower to run a heavy load, but unless the motor is used over a period of time, there will be no energy conversion The energy (W) lost or gained by any system is therefore determined by The unit of energy is the wattsecond or joule

Energy The wattsecond, however, is too small a quantity for practical purposes, so watthour (Wh) and kilowatthour (kWh) were defined, as follows: To develop some sense, consider 1 kWh energy is dissipated by a 100-W bulb in 10 h.

Energy – Kilowatthour Meter The kilowatthour meter is an instrument for measuring the energy supplied to the residential or commercial user of electricity It is normally connected directly to the lines at a point just prior to entering the power distribution panel of the building

Energy – Kilowatthour Meter Example – How long can a 205-W television set be on before using more than 4 kWh of energy? Solution:

Energy – Kilowatthour Meter Example – What is the cost of using a 5-hp motor for 2 h if the rate is 9¢ per kilowatthour? Solution:

Energy – Kilowatthour Meter Example – What is the total cost of using all of the following at 9¢ per kilowatthour? –A 1200-W toaster for 30 min –Six 50-W bulbs for 4 h –A 400-W washing machine for 45 min –A 4800-W electric clothes dryer for 20 min Solution:

Circuit Breakers, GFCIs and Fuses To save the costly equipments from short circuit and thus limit the current level, fuses or circuit breakers are installed in panels where the power enters the house or installation from outside feeder lines The fuses have an internal metallic conductor through which the current will pass; a fuse will begin to melt if the current through the system exceeds the rated value

Circuit Breakers, GFCIs and Fuses In homes built in recent years, fuses have been replaced by circuit breakers When the current exceeds rated conditions, an electromagnet in the device will have sufficient strength to draw the connecting metallic link in the breaker out of the circuit and open the current path When conditions have been corrected, the breaker can be reset manually

Circuit Breakers, GFCIs and Fuses Note the load on each breaker should not exceed 80% of its rating, 15 A circuit breaker to 12 A 20 A circuit breaker to 16-A 30 A circuit breaker to 24-A

Circuit Breakers, GFCIs and Fuses GCFIs (ground fault current interrupt) are designed to trip more quickly than the standard circuit breaker. The commercial unit trips in 5 ns and are generally employed in bathroom and other sensitive areas. The GFCI is able to react as quickly by sensing the difference between input and output currents to outlet An errant path such as through an individual establishes a difference in the two current levels and causes breaker to trip and disconnect power source

Applications – Microwave Oven Most microwaves are rated at 500 W to 1200 W at a frequency of 2.45 GHz (2.45 billion cycles per second) The heating occurs because water molecules in food are vibrated at such a high frequency that the friction with neighbouring molecules causes the heating effect

Applications – Microwave Oven

The microwave uses a 120 / 220 V ac supply which is then converted through a high voltage transformer to one having peak values approaching 5000 V (at substantial current levels) Through the rectifying process, a high dc voltage of a few thousand volts will be generated that will appear across a magnetron. The magnetron (initially invented for WWII radar units), will generate the required 2.45-GHz signal for oven

Applications – Microwave Oven If the microwave is plugged into a 120-V outlet, the current drawn is I = P/V = 1200 W/120 V = 10.0 A The amount of power dedicated solely to the cooking process is determined by efficiency level. That is, P o = ηP i = (0.55)(1200 W) = 660 W The energy transferred to the food over a period of 5 min can then be determined from W = Pt = (660 W)(5 min)(60 s/1 min) = 198 kJ

Applications – Microwave Oven The number of kilowatthours drawn by the unit is determined from W = Pt/1000 = (1200 W)(5/60 h)/1000 = 0.1 kWh At a rate of 10 Rs / kWh we find that we can cook the food for 1 Rs — relatively speaking, pretty cheap However, the cooking time with a microwave oven is related to the amount of food in the oven, also it is not a linear relationship so it won’t take twice as long — perhaps 75% to 90% longer time thus raising cost.

Applications – Household Wiring One specification that defines household wiring is the maximum current that can be drawn from the power lines since the voltage is fixed at 110 V or 220 V. For most homes a 100-A service is the normal. Today, with all the electronic systems becoming commonplace in home, many people are opting for 200-A service. A 100-A service specifies that the maximum current that can be drawn through power lines into your home is 100 A.

Applications – Household Wiring Using the line-to-line rated voltage and the full-service current we can determine the maximum power that can be delivered using the basic power equation: P = EI = (208 V)(100 A) = 20,800 W = 20.8 kW This rating reveals that total rating of all units turned on in the home cannot exceed 20.8 kW at any one time. If it did, we could expect the main breaker at the top of the power panel to open or even cause damage to transformers.

Solution to Problems # 13 a)If an electric heater draws 9.5 A when connected to a 120-V supply, what is internal resistance of heater? b)How much energy is converted in 1 h? Solution:

Solution to Problems # 33 - A calculator with an internal 3-V battery draws 0.4 mW when fully functional. a)What is the current demand from the supply? b)If the calculator is rated to operate 500 h on the same battery, what is the ampere-hour rating of the battery? Solution:

Solution to Problems # 48 – If the total input and output power of two systems in cascade are 400 W and 128 W, respectively, what is the efficiency of each system if one has twice the efficiency of the other? Solution:

Chapter 5 - Introduction Two types of currents Direct current (dc), in which ideally the flow of charge (current) does not change in magnitude (or direction) with time. Sinusoidal alternating current (ac), in which the flow of current is continually changing in magnitude (and direction) with time. In this semester we will restrict to circuit analysis purely from a dc approach.

Chapter 5 - Introduction we generally consider the wire to be an ideal conductor (that is, having no opposition to flow) The current is limited only by the resistor R The higher the resistance, the less the current, and conversely, as determined by Ohm’s law.

Series Circuit A circuit consists of any number of elements joined at terminal points, providing at least one closed path through which charge can flow. If all the elements are in series, the network is called a series circuit A branch of a circuit is any portion of the circuit that has one or more elements in series

Series Circuit Two elements in a circuit are in series if 1)They have only one terminal in common (i.e., one lead of one is connected to only one lead of the other). 2)The common point between the two elements is not connected to another current-carrying element.

Series Circuit Note that the current is the same through series elements. The total resistance of a series circuit is the sum of the resistance levels.

Series Circuit Note that the total resistance is actually the resistance “seen” by the battery as it “looks” into the series combination of elements The only resistance the source “sees” is the total resistance. It is totally unaware of how the elements are connected to establish R T R T of N resistors of same value in series is

Series Circuit Once R T is known, the current drawn from the source can be determined using Ohm’s law, Since E is fixed, the magnitude of the source current will be totally dependent on the magnitude of R T. A larger R T will result in a relatively small value of I s, while lesser values of R T will result in increased current levels

Series Circuit The fact that the current is the same through each element permits a direct calculation of the voltage across each resistor using Ohm’s law; that is,

Series Circuit The power delivered to each resistor can be calculated, e.g for R 1 The power delivered by the source is The total power delivered to a resistive circuit is equal to the total power dissipated by the resistive elements.

Series Circuit - Example a)Find the total resistance for the series circuit of fig. b)Calculate the source current I s. c)Determine the voltages V 1, V 2, and V 3. d)Calculate the power dissipated by R 1, R 2, and R 3. e)Determine the power delivered by the source, and compare it to the total power dissipated.

Series Circuit – Solution to Example a)Find the total resistance for the series circuit of fig. b)Calculate the source current I s. c)Determine the voltages V 1, V 2, and V 3.

Series Circuit – Solution to Example d)Calculate the power dissipated by R 1, R 2, and R 3. e)Determine the power delivered by the source, and compare it to the total power dissipated.

Series Circuit - Example Example – Given R T and I, calculate R 1 and E for the circuit of fig. Solution:

Voltage Sources in Series Voltage sources can be connected in series to increase or decrease the total voltage applied to a system The net voltage is determined simply by summing the sources with the same polarity and subtracting the total of the sources with the opposite “pressure.” The net polarity is the polarity of the larger sum.

Summary / Conclusion Chapter 4 Energy Circuit Breakers, GFCIs and Fuses Applications Solutions to Problems Chapter 5 Introduction Series Circuit Voltage Sources in Series