ELECTRICITY & MAGNETISM (Fall 2011)

ELECTRICITY & MAGNETISM (Fall 2011) LECTURE # 9 BY MOEEN GHIYAS

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

Today’s Lesson Contents • Ohm’s Law • Power • Wattmeters • Efficiency

Ohm’s Law – Chapter 4 • Effect = Cause / Opposition • Where Effect = Flow of charge (Current) Cause = Potential Difference (Voltage) Opposition = Resistance • I = V / R or V = I R

Ohm’s Law • I = V / R or V = I R • Note the following: • The symbol ‘E’ for the voltage of the battery (a source of electrical energy), • Whereas the loss in potential energy across the resistor is given by symbol ‘V’ • The polarity of the voltage drop across the resistor is as shown

Ohms Law • Ohms Law Pie I = V / R V = I x R V V ? I ? I R R R

Ohm’s Law • Example – Determine the current resulting from the application of a 9-V battery across a network with a resistance of 2.2Ω • Solution:

Ohm’s Law • Example – Calculate the voltage that must be applied across the soldering iron of Fig to establish a current of 1.5 A through the iron if its internal resistance is 80Ω. • Solution:

Plotting Ohms Law Fixed Resistance Variable Resistance y = m * x + b (st line eqn) I = 1/R * E + 0 Slope = m = 1/R V (Volts)

Plotting Ohms Law

Plotting Ohm’s Law • Example – Determine the resistance associated with the curve of Fig. • Solution:

Ohm’s Law Application on Diode • Diode is a semiconductor device acts like a switch • Offers low-resistance path to current in one direction and a high resistance to current in reverse direction • Confirmation using Ohm’s Law

Power • Work is done in converting an energy into another form of energy e.g. mechanical into mechanical or electrical to mechanical or heat energy etc. For example rotating the spindle of a motor physically by hand or electrically. • Power is defined as the work done in a specified amount of time, i.e. a rate of doing work. • Energy (W for work done) is measured in joules (J) • Time in seconds (s), • Power is measured in joules/second (J/s). • The electrical unit of measurement for power is the watt (W) Note: W for Energy, and W for Watt (Power)

Power • The unit of measurement, the watt, is derived from the surname of James Watt • He introduced the horsepower (hp) as a measure of the average power of a strong dray horse over a full working day. It is approximately 50% more than can be expected from the average horse. • The horsepower and watt are related in the following manner:

Power • Now for power, • The power delivered to, or absorbed by, an electrical device or system can be found in terms of the current and voltage by substituting their values in terms of charge in coulomb and potential energy in joules.

From Chapter 2, we know for voltage • If a mass (m) is raised to some height (h) above a reference plane, it has a measure of potential energy expressed in joules (J) that is determined by • where g is the gravitational acceleration (9.754 m/s2). This mass now has the “potential” to do work such as crush an object placed on the reference plane. • Algebraic manipulation in respect of charge gives,

From Chapter 2, we know for voltage • In general, the potential difference between two points is determined by • A potential difference of 1 volt (V) exists between two points if 1 joule (J) of energy is exchanged in moving 1 coulomb (C) of charge between the two points. • The unit of measurement volt (V) was chosen to honour Alessandro Volta

From Chapter 2, we know for current • The current in amperes can now be calculated using the following equation: • The capital letter I was chosen from the French word for current: intensité.

Power • Now for power, • The power delivered to, or absorbed by, an electrical system can be found in terms of the current and voltage by substituting their values in terms of charge in coulomb and potential energy in joules. Therefore, • . Where • Thus we have

Power • Power or Pie wheel I = P / E P = I x E P P ? I ? I E E E

Power • By direct substitution of Ohm’s law, the equation for power can be obtained in two other forms: • . or • Also • . or

Power and Ohms Law Wheel • Circular wheel Watts Amperes E/ R E2 / R W / E I2 R √ W / R I E P I E R E / I W R E2 / W W / I W / I2 I R Ohms Volts

Power • Power can be delivered or absorbed as defined by the polarity of the voltage and the direction of the current. • Note that the current has the same direction as established by the source delivering the power in a single-source network. But in multisource network, the battery may be absorbing power e.g. when battery is being charged.

Power • For resistive elements, all the power delivered is dissipated in the form of heat • Current will always enter the terminal of higher potential corresponding with the absorbing state. • A reversal of the current direction will also reverse the polarity of the voltage across the resistor.

Power • Example – Find the power delivered to the dc motor • Solution:

Power • Example – Determine current through a 5-kΩ resistor when the power dissipated by the element is 20 mW. • Solution:

Wattmeters • Can we measure power, like we do with: • voltmeters for voltage, • ampmeter for current and • ohmmeter for resistance? • If yes, how many terminals required in meter?

Wattmeters • Three voltage terminals may be available on the voltage side to permit a choice of voltage levels. • On most wattmeters, the current terminals are physically larger than the voltage terminals to provide safety and to ensure a solid connection.

Wattmeters • If the current coils (CC) and potential coils (PC) of the wattmeter are connected as shown in Fig, there will be an up-scale reading on the wattmeter. A reversal of either coil will result in a below-zero indication.

Efficiency • Note that output energy level are always less than the applied energy due to losses and storage within system

Efficiency • Conservation of energy requires that: • Energy input = Energy output + Energy lost or stored • Dividing both sides of the relationship by t gives • Since P = W / t, we have

Efficiency • The efficiency (η) of the system is then determined by: • . or • where η is a decimal number, but usually expressed as a percentage • In terms of the energy, the efficiency in percent is:

Efficiency • The maximum possible efficiency is 100%, which occurs when Wo = Wi or Po = Pi, or in other words when power lost or stored in the system is zero. • Obviously, the greater the internal losses of the system in generating the necessary output power or energy, the lower the net efficiency.

Efficiency • Example – A 2-hp motor operates at an efficiency of 75%. Whatis the power input in watts? If the applied voltage is 220 V, what is the input current? • Solution:

Efficiency • Example – If η = 0.85, determine the output energy level if the applied energy is 50 J • Solution:

Efficiency • The very basic components of a generating (voltage) system are depicted in Fig

Efficiency • The efficiency of each system is given by • If we form the product of these three efficiencies,

Efficiency • If we form the product of these three efficiencies, • but Pi2 = Po1 and Pi3 = Po2 , so quantities above cancel, • we get Po3 /Pi1, which is efficiency of the entire system. • In general, for the cascaded system of Fig

Efficiency • Example – Find the overall efficiency of the system of Fig. 4.19 if η1 = 90%, η2 = 85%, and η3 = 95%. Later, if the efficiency η1 drops to 40%, find the new overall efficiency and compare the result. -------- Solution: • The total efficiency of a cascaded system is therefore determined primarily by lowest efficiency (weakest link)

Summary / Conclusion • Ohm’s Law • Power • Wattmeters • Efficiency

ELECTRICITY & MAGNETISM (Fall 2011)