Applied Circuit Analysis

Chapter 3 -Power and Energy

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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)

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WP

t

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)

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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:

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P VI

22 V

P I R PR

V, I, R, and Power

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

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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.

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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.

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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.

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Resistor Power Ratings II

• The common carbon or metal film resistors come in ratings ranging from 1/8th W to 2 W.

• The most commonly found are either the 1/8th or the ¼ W.

• Resistors with power rating above 2W are wirewound.

• These can range from 5W to 200W

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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.

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Efficiency II• Efficiency (η) can be expressed in

terms of power:

• Or in terms of energy

• In both cases it may never exceed 100%

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100%out

in

P

P

100%out

in

W

W

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.

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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.

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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.

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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”

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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.

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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.

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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.

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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)

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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.

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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.

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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.

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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.

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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.

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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.

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Watt-hour meter

• The watt-hour meter shown should be familiar to everyone.

• It will measure accumulated kilowatt-hours.

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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.

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