# Applied Circuit Analysis Chapter 3 - Power and Energy Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Applied Circuit Analysis Chapter 3 - Power and Energy Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Power and Energy Energy (E) is the ability to do work Power (P) is the rate of expending energy They are related as follows: Where t is time in seconds Power is measured in Watts (W) while energy is measured in Joules (J) 2

Other Units Another familiar unit of measurement for power is the horsepower (hp) This unit was introduced by James Watt One hp is equal to approximately 0.75kW Electric companies, commonly measure energy with power x time The unit used is typically the watt-hour (Wh) kilowatt-hour (kWh) 3

Power in Electric Circuits In a circuit, power is defined by the product of current and voltage: If we incorporate Ohm’s law (V=IR), we can express power in terms of other circuit quantities: 4

V, I, R, and Power The four parameters, V, I, R, and P can be related to each other as shown: 5

Power Sign Convention Current direction and voltage polarity determine the sign of the power in a circuit element. In passive sign convention, power is positive when current enters the positive terminal of the element. 6

Passive Sign Convention In this convention, positive power represents the situation where the element in question is absorbing energy. When the power is negative (like shown), the element is supplying power. 7

Resistor Power Ratings In addition to the value of resistance, a resistor usually has a rating for its power specified. This rating is the maximum power it can handle without it becoming too hot or risking damage to it. The power rating is dependent on its physical size; the larger the size, the more power it can handle. 8

Resistor Power Ratings II The common carbon or metal film resistors come in ratings ranging from 1/8 th W to 2 W. The most commonly found are either the 1/8 th or the ¼ W. Resistors with power rating above 2W are wirewound. These can range from 5W to 200W 9

Efficiency The efficiency of a device is a means of comparing its useful output to the input required to run it. In a device, some of the input power will be “lost” in a form that is unusable. This is typically in the form of heat. 10

Efficiency II Efficiency (η) can be expressed in terms of power: Or in terms of energy In both cases it may never exceed 100% 11

Fuses As we know, power dissipated in resistors varies as the square of the current. Wiring in buildings, though very conductive, is not without some resistance. If excess current passes through the wires, they will heat up and potentially ignite surrounding materials. 12

Fuses II To prevent this from happening, protective devices are required, which will interrupt the flow of current. The most basic protective device is the fuse. Fuses are single use devices that create an open circuit when current exceeds their rated value. 13

Fuses III A fuse consists of a thin metal wire enclosed in a cartridge, which is inserted into a receptacle built within the circuit. In its pristine state, the fuse has very low resistivity (it may read 0 Ohms on an ohmmeter). In this state, it conducts current to the circuit as would a wire. 14

Blown Fuse Each fuse has a specifically designed thickness of wire that will heat up as the current through it increases. At the rated value, the wire will melt, and result in a broken connection, thus halting the flow of current. This is referred to as a “blown fuse ” 15

Causes of blown fuses One of the most common causes for a blown fuse is the sudden development of a short circuit. –This may be due to the introduction of a conducting object (screwdriver across terminals) –It may also be due to failure of a component, such as a capacitor. Another cause is too many loads drawing too much current. 16

Circuit Breaker Fuses for the most part continue to be used in electronic appliances. In households, however, it is far more common now for a more advanced protective device to be used: The circuit breaker. The function remains the same, current exceeding the rated value causes an open circuit. 17

Circuit Breaker II The key difference is that unlike a fuse, the circuit breaker can be reset. It works by using a spring that expands with heat. When heated beyond a specified point, a switch is activated that opens the circuit. The breaker can then be manually reset. 18

Ground Fault Fuses and circuit breakers are designed to protect buildings and equipment from damage due to too much current. They are not effective in protecting people from receiving shocks however. There does exist a protective device that serves that role. It is called the ground fault circuit interrupter (GFCI) 19

Ground Fault II The concept of grounding was developed to protect against electric shock. But in certain situations current can flow along the ground path. 20

Ground Fault III The situation that comes to mind most readily is an appliance falling into a bathtub. If a person becomes part of the return path injury or death can occur. Recall that only a few tens of mA are required for injury. This is not enough to trigger a fuse or circuit breaker. 21

GFCI The GFCI operates by sensing the current leakage. The current along the hot wire and neutral wire are compared. If any difference is sensed then current may be passing through the ground path. If so, the GFCI breaks the circuit just like a circuit breaker. 22

GFCI II They can either be in wall outlets or installed at the circuit breaker to protect an entire building. A typical wall outlet version is shown here. 23

Wattmeter Power consumption in a AC system can be measured using a Wattmeter. The meter consists of two coils; the current and voltage coils. The current coil is designed with low impedance and is connected in series with the load. The voltage coil is designed with very large impedance and is connected in parallel with the load. 24

Wattmeter II The induced magnetic field from both causes a deflection in the current coil. Ideally, the configuration does not alter the load and affect the power measured. The physical inertia of the moving coil results in the output being equal to the average power. 25

Watt-hour meter The watt-hour meter shown should be familiar to everyone. It will measure accumulated kilowatt-hours. 26

Watt-hour meter The meter works by using a motor who torque is proportional to the current flowing through it. The motor turns a register that counts the number of revolutions the motor makes. This, though a series of gears moves dials indicating the energy used. 27

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