Electromagnetism Lecture#07-11 MUHAMMAD MATEEN YAQOOB THE UNIVERSITY OF LAHORE SARGODHA CAMPUS.

Electromagnetism

Lecture#07-11MUHAMMAD MATEEN YAQOOB

THE UNIVERSITY OF LAHORE

SARGODHA CAMPUS

MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

OHM’s LAW The most important fundamental law in electronics is Ohm’s law, which relates voltage, current, and resistance.

Georg Simon Ohm (1787-1854) studied the relationship between voltage, current, and resistance and formulated the equation that bears his name. In terms of current, Ohm’s law states

VI

R


THE RELATIONSHIP OF CURRENT, VOLTAGE, AND RESISTANCE

I α V Constant Resistance

Effect on the current of changing the voltage with the resistance at a constant value.

Less V, less I More V, More I


THE RELATIONSHIP OF CURRENT, VOLTAGE, AND RESISTANCE

I α 1/R Constant Voltage

Effect on the current of changing the resistance with the voltage at a constant value.

Less R, more I More R, less I


OHM’s LAW Ohm's law states that current is directly proportional to voltage and inversely proportional to resistance.

I α V Constant Resistance

I α 1/R Constant Voltage

where: I = current in amperes (A) V = voltage in volts (V) R = resistance in ohms (Ω)


Ohm’s Law power consumption through a resistance

Some practical every day examples of this basic rule are: base board heaters, electric frying pans, toasters and electric light bulbs. The heater consumes power producing heat for warmth, the frying pan consumes power producing heat for general cooking, the toaster consumes power producing heat for cooking toast, and the electric light bulb consumes power producing heat and more important light. A further example is an electric hot water system. All are examples of Ohm’s Law.


The Linear Relationship of Current and Voltage

In resistive circuits, current and voltage are linearly proportional. Linear means that if one of the quantities is increased or decreased by a certain percentage, the other will increase or decrease by the same percentage, assuming that the resistance is constant in value.

V= 10V, V=30V


Example Assume that you are measuring the current in a circuit that is operating with 25 V. The ammeter reads 50 mA. Later, you notice that the current has dropped to 40 mA. Assuming that the resistance did not change, you must conclude that the voltage source has changed. How much has the voltage changed, and what is its new value?


CALCULATING CURRENT How many amperes of current are in the following circuit?


Units with Metric Prefixes

In electronics, resistance values of thousands of ohms or even millions of ohms are common.

Example

Calculate the current.


CALCULATING VOLTAGE In the circuit of following Figure, how much voltage is needed to produce 5 A of current?


CALCULATING VOLTAGE How much voltage will be measured across the resistor ?


CALCULATING RESISTANCE In the circuit of following Figure, how much resistance is needed to draw 3.08 A of current from the battery?


Which circuit in Figure has the most current? The least current?

15.2 mA, 19.2 mA, 21.3 mA


ENERGY AND POWER Energy is the ability to do work.

Power is the rate at which energy is used.

Where

P = power in watts (W)

W = energy in joules (J)

t = time in seconds (s)One watt (W) is the amount of power when one joule of energy is used in one second.


An amount of energy equal to 100 J is used in 5 s. What is the power in watts?


The Kilowatt-hour (kWh) Unit of Energy

Determine the number of kilowatt-hours (kWh) for each of the following energy consumptions:

(a) 1400 W for 1 h (b) 2500 W for 2 h (c) 100,000 W for 5 h


POWER IN AN ELECTRIC CIRCUIT

The amount of power dissipated in an electric circuit is dependent on the amount of resistance and on the amount of current, expressed as follows:

P=I2R

Power dissipation in an electric circuit results in heat energy given off by the resistance.


POWER IN AN ELECTRIC CIRCUIT Watt’s Laws


Calculate the power in each of the following three circuits.

20W, 188W, 2.5W


RESISTOR POWER RATINGS The power rating is the maximum amount of power that a resistor can dissipate without being damaged by excessive heat buildup.

The power rating of a resistor is directly related to its surface area.


Determine whether the resistor in each circuit of following has possibly been damaged by overheating.

0.810W, 0.384 W, 2.5W


POWER SUPPLIES Ampere-hour Ratings of Batteries

Batteries convert chemical energy into electrical energy. Because of their limited source of chemical energy, batteries have a certain capacity that limits the amount of time over which they can produce a given power level. This capacity is measured in ampere-hours.


Ampere-hour Ratings of Batteries

The ampere-hour (Ah) rating determines the length of time that a battery can deliver a certain amount of average current to a load at the rated voltage.

For example, a 12 V automobile battery may be rated

for 70 Ah at 3.5 A. This means that it can produce an average of 3.5 A for 20 h at the rated voltage.


RESISTORS IN SERIES When connected in series, resistors form a "string" in which there is only one path for current.

A series circuit provides only one path for current between two points so that the current is the same through each series resistor.


CURRENT IN A SERIES CIRCUIT The current is the same through all points in a series circuit.


TOTAL SERIES RESISTANCE The total resistance of a series circuit is equal to the sum of the resistances of each individual series resistor.

Total resistance increases with each additional series resistor


Series Resistance Formula For any number of individual resistors connected in series, the total resistance is the sum of each of the individual values.

Where n= 1,2,3……………….

RT = R1 + R2 + R3 + ... + Rn


Determine the value of R4 in the circuit of following figure?

1OkΩ


Equal-Value Series Resistors When a circuit has more than one resistor of the same value in series, there is a shortcut method to obtain the total resistance:

RT = nR

where n is the number of equal-value resistors and R is the resistance value.

Find the RT of eight 22 Ω resistors in series.

176 Ω


APPLICATION OF OHM'S LAW The basic concepts of series circuits and Ohm's law can be applied to series circuit analysis.

1. Current through any of the series resistors is the same as the total current.

2. If you know the total applied voltage and the total resistance, you can determine the total current by Ohm's law.

3. If you know the voltage drop across one of the series resistors (Rx ), you can determine the total current by Ohm's law.


APPLICATION OF OHM'S LAW4. If you know the total current, you can find the voltage drop across any of the series resistors by Ohm's law.

5. The polarity of a voltage drop across a resistor is positive at the end of the resistor that is closest to the positive terminal of the voltage source.

6. The current through a resistor is defined to be in a direction from the positive end of the resistor to the negative end.

7. An open in a series circuit prevents current; and, therefore, there is zero voltage drop across each series resistor. The total voltage appears across the points between which there is an open.


SERIES CIRCUIT ANALYSIS Find the current in the given circuit.

129Ω, 194mA


RESISTORS IN PARALLEL When two or more resistors are individually connected between two separate points, they are in parallel with each other. A parallel circuit provides more than one path for current.

Each current path is called a branch, and a parallel circuit is one that has more than one branch.

Resistors in parallel.


Calculate the total parallel resistance between points A and B of the circuit in the following Figure.


The Case of Two Resistors in Parallel

The total resistance for two resistors in parallel is equal to the product of the two resistors divided by the sum of the two resistors.


The Case of Equal-Value Resistors in Parallel


KIRCHHOFF'S CURRENT LAW Kirchhoff's voltage law deals with voltages in a single closed path. Kirchhoff’s current law applies to currents in multiple paths.

Kirchhoff's current law, often abbreviated KCL, can be stated as follows:

‘’The sum of the currents into a node (total current in) is equal to the sum of the currents out of that node (total current out)’’.


KIRCHHOFF'S CURRENT LAW A node is any point or junction in a circuit where two or more components are connected. In a parallel circuit, a node or junction is a point where the parallel branches come together.

Node A

Node B


Generalized circuit node illustrating Kirchhoff's current law.

The algebraic sum of all the currents entering and leaving a node is equal to zero.


The branch currents are shown in the circuit of following Figure. Determine the total current entering node A and the total current leaving node B.


Determine the current I2 through R2 in the following Figure.


Use Kirchhoff's current law to find the current measured by ammeters A3 and A5 in the following Figure.


Determine the current through each resistor in the parallel circuit of following Figure.


Find the voltage Vs across the parallel circuit in the given circuit.


CURRENT DIVIDERS A parallel circuit acts as a current divider because the current entering the junction of parallel branches "divides" up into several individual branch currents.

Total current divides between the two branches.


Current-Divider Formula


Current-Divider formulas for Two Branches


Find I1 and l2 in the following Figure.


Some Important Formulas related to Parallel Circuits


KIRCHHOFF'S VOLTAGE LAW The sum of all the voltage drops around a single closed path in a circuit is equal to the total source voltage in that loop.

Vs = V1 + V2 + V3 + ... + Vn


VOLTAGE DIVIDERS A circuit consisting of a series string of resistors connected to a voltage source acts as a voltage divider.

Two-resistor voltage divider.


Voltage-Divider Formula

Vx = (Rx/Rt)Vs

The voltage drop across any resistor or combination of resistors in a series circuit is equal to the ratio of that resistance value to the total resistance, multiplied by the source voltage.


Problems related to Kirchhoff's Voltage Law

Q.1 Five resistors are in series with a 20 V source. The voltage drops across four of the resistors are 1.5 V, 5.5 V, 3 V, and 6 V. How much voltage is dropped across the fifth resistor?


Q.2 Determine the unspecified voltage drop(s) in the circuit of following Figure. Show how to connect a voltmeter to measure each unknown voltage drop.


Problems related to Voltage Dividers Q.1 The total resistance of a circuit is 560Ω. What percentage of the total voltage appears across a 27 Ω resistor that makes up part of the total series resistance?


Q.2 Determine the voltage with respect to ground for output A, B, and C in the following Figure.


CIRCUIT THEOREMS AND CONVERSIONS Till now, we have analyzed various types of circuits using Ohm's law and Kirchhoff's laws. Some types of circuits are difficult to analyze using only those basic laws and require additional methods in order to simplify the analysis.

The theorems and conversions in this lecture make analysis easier for certain types of circuits. These methods do not replace Ohm's law and Kirchhoff's laws, but they are normally used in conjunction with the laws in certain situations.


CIRCUIT THEOREMS AND CONVERSIONS

The DC Voltage Source

The Current Source

Source Conversions

The Superposition Theorem


THE DC VOLTAGE SOURCE The DC voltage source is one of the principal types of energy source in electronic applications, so it is important to understand its characteristics. The dc voltage source ideally provides constant voltage to a load even when the load resistance varies. The ideal voltage source has an internal resistance of zero. Rs=0Ω

Ideal dc voltage source.


THE DC VOLTAGE SOURCE All voltage sources have some inherent internal resistance as a result of their physical and/or chemical makeup, which can be represented by a resistor in series with an ideal source,

Practical voltage source.


THE CURRENT SOURCE The current source is another type of energy source that ideally provides a constant current to a load even when the resistance of the load varies. The ideal current source has an infinitely large internal parallel resistance.

Ideal current source.


THE CURRENT SOURCE

Practical current source with load.


SOURCE CONVERSIONS In circuit analysis, it is sometimes useful to convert a voltage source to an equivalent current source, or vice versa.

Converting a Voltage Source to a Current Source


SOURCE CONVERSIONS Terminal equivalencyEquivalency of two sources means that for any given load resistance connected to the two sources, the same load voltage and load current are produced by both sources. This concept is called Terminal equivalency.


ExampleConvert the voltage source in the Figure to an equivalent current

source and show the equivalent circuit.


Converting a Current Source to a Voltage Source


ExampleConvert the current source in the Figure to an equivalent voltage source and

show the equivalent circuit.

Electromagnetism Lecture#07-11 MUHAMMAD MATEEN YAQOOB THE UNIVERSITY OF LAHORE SARGODHA CAMPUS.

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