electromagnetism lecture#7 instructor: engr. muhammad mateen yaqoob

ElectromagnetismLecture#7

Instructor:

Engr. Muhammad Mateen Yaqoob

MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

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.


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 through each resistor in the parallel circuit of following Figure.


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


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?


Circuit Excitation Source-free circuits (free of independent sources)

DC Source excitation (independent sources)


FIRST-ORDER CIRCUIT Three passive elements (resistors, capacitors, and inductors) individually,

Circuits having various combinations of two or three of the passive elements.

RC and RL circuits. Analysis of RC and RL circuits by applying Kirchhoff’s laws. The differential equations resulting from analyzing RC and RL circuits are of the first order. Hence, the circuits are collectively known as first-order circuits.


THE SOURCE-FREE RC CIRCUIT


The natural response of a circuit refers to the behavior (in terms of voltages and currents) of the circuit itself, with no external sources of excitation.

The voltage response of the RC circuit.


The time constant of a circuit is the time required for the response to decay by a factor of 1/e or 36.8 percent of its initial value.

The voltage response of the RC circuit.


The Key to Working with a Source - free RC Circuit is

Findin g :

1. The initial voltage v(0) = V0 across the capacitor.

2. The time constant τ .

vC(t) = v(t) = v(0)e−t/τ

other variables

Capacitor current iC

Resistor voltage vR

Resistor current iR

can be determined.


Applications of RC and RL circuits

RC and RL Circuits have many applications in the field of Electrical, Electronics, Communication, Computer Engineering, Signal Processing and so on

These circuits have many practical applications, some of their major applications are listed below:

1. Amplifiers

2. Oscillators

3. Filters

4. Switching Regulator

5. Tuned Amplifiers

6. Radio Transmitter and Receiver

7. TV Receiver

electromagnetism lecture#7 instructor: engr. muhammad mateen yaqoob

Documents

node total current

value resistors

current path

total voltage

parallel circuit

series resistors rx

total applied voltage

given circuit