1. Electromagnetism Lecture#7 Instructor: Engr. Muhammad Mateen Yaqoob

2. Determine the value of R 4 in the circuit of following figure? 1OkΩ MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

3. 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: R T = nR where n is the number of equal-value resistors and R is the resistance value. Find the R T of eight 22 Ω resistors in series. 176 Ω MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

4. 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. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

5. APPLICATION OF OHM'S LAW 4. 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. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

6. SERIES CIRCUIT ANALYSIS Find the current in the given circuit. 129Ω, 194mA MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

7. 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. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

9. 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. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

10. The Case of Equal-Value Resistors in Parallel MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

11. 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)’’. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

12. 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 MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

13. Generalized circuit node illustrating Kirchhoff's current law. The algebraic sum of all the currents entering and leaving a node is equal to zero. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

14. 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. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

15. Determine the current through each resistor in the parallel circuit of following Figure. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

16. Find the voltage Vs across the parallel circuit in the given circuit. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

17. 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 = V 1 + V 2 + V 3 +... + Vn MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

18. 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. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

19. 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. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

20. Problems related to Kirchhoff's Voltage Law Q.1Five 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? MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

21. Q.2Determine the unspecified voltage drop(s) in the circuit of following Figure. Show how to connect a voltmeter to measure each unknown voltage drop. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

22. Problems related to Voltage Dividers Q.1The 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? MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

23. Circuit Excitation Source-free circuits (free of independent sources) DC Source excitation (independent sources) MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

24. 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. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

25. THE SOURCE-FREE RC CIRCUIT MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

27. 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. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

28. 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. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

29. The Key to Working with a Source - free RC Circuit is Findin g : 1. The initial voltage v(0) = V 0 across the capacitor. 2. The time constant τ. v C (t) = v(t) = v(0)e −t/τ other variables Capacitor current i C Resistor voltage v R Resistor current i R can be determined. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

30. 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 MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE