DC Circuits Lecture Notes PDF

UNIT 1: DC CIRCUITS Content: 1. Electrical Circuit 2. Network Components 3. Resistance 4. Capacitance 5. Inductance 6. HW Problems 1. Electrical Circuit  Charge and Charg Current Charge is an property e: of the atomic...

UNIT 1: DC CIRCUITS Content: 1. Electrical Circuit 2. Network Components 3. Resistance 4. Capacitance 5. Inductance 6. HW Problems 1. Electrical Circuit  Charge and Charg Current Charge is an property e: of the atomic electrical particles of a matter. S.I Unit: Coulomb (C) Symbol: Q Current: Rate of change of charge. OR Continuous o flow electrons in an f electrical circuit. S.I Unit: Ampere (A) Symbol: I  Charge and Current 𝑑 𝑡 Mathematica 𝐼 𝑄 𝑜𝑟 𝑄 = ∫ 𝑑 lly, = 𝐼. 𝑑𝑡 Or, in simple 𝑡 𝑡0 𝐼 terms: = So, 1 Ampere = 1 coulomb/ 1 second.  Volta ge It is the energy (Work) required to move a unit charge through an element. S.I Unit: Volt (V) Symbol: V  Power and Energy Power: Rate at which the work is done. OR Time rate of absorbing or supplying energy S.I Unit: Watts 𝑃 =𝑑𝑡 𝑑=𝑞. 𝑑𝑊 𝑑𝑊 𝑑𝑞 (W) Symbol: P = 𝑉.𝐼 𝑑𝑡 Mathematically, 𝑃= 𝑉. 𝐼 Implie s,  Power and Energy Energy: Capacity of doing work. S.I Unit: Energy (E): E = P * t Joules(J) E = V * I * t Symbol: E  2. Network Components Active Passive Batte ry Resistance (R) Transistor, Capacitance Op-amp, (C) Diode Inductance VS and CS (L) Generators Transformer s  3. Resistance Resistance: It is an opposition to the flow of current. S.I Unit: Ohm (Ω) Symbol: R  The units of resistance is Ohms, which is indicated by Ω omega. The formula for resistance is R = V/I It would really be difficult to manufacture the resistors with each and every value. Few values are chosen and the resistors of such values are only manufactured. These are called as “Preferred Values”. Tolerance is the range of value up to which a resistor can withstand without getting destroyed. This is an important factor. Resistor Color Code The power rating is not indicated in the resistor color code and must be determined by experience using the physical size of the resistor as a guide. For resistors with 5% or 10% tolerance, the color code consists of 4 color bands. For resistors with 1% or 2% tolerance, the color code consists of 5 bands.  4-Band Resistors The resistor nominal value is encoded in the color code in Powers of Ten Notation. The template for determining the nominal value and tolerance of a resistor with 4 color bands is given below: 1st Band = 2nd Band = 3rd Band = 4th Band = 1st Significant Digit 2nd Significant Digit Multiplier Tolerance ___ ___  10    ____ % How do we know which color corresponds to which number? Answer: Using the Resistor Color Code Table  Example 1. Determine the nominal resistance value and the tolerance for the resistor shown below. Solution: Brown =1 Black =0 Red =2 Gold = 5% 2 1___ 0___  10    ____5% Nominal value = 10102 = 1,000 Tolerance = 5%.  It is typical to express the resistance value in: k if the resistance  1,000 M if the resistance  1,000,000. To convert from  to k,  to M, or vice-versa, use the table below: In the previous example we would say the resistor has a nominal value of: 1,000W =1kW 1,000 Example 2. a) Determine the nominal value and tolerance for the resistor below. b) What is the minimum resistance value this resistor can actually have? c) What is the maximum resistance value this resistor can actually have? Yellow =4 Violet =7 Orange =3 Gold = 5% Solution: 3 4___ 7___  10   ____ 5% Resistor nominal value = 47103 = 47,000 = 47k. Tolerance = 5% Solution: continued Minimum resistance value: Multiply the nominal value by the tolerance and then subtract this from the nominal value: nominal value – nominal value * tolerance = 47kW- 47kW*0.05 = 47kW- 2.35kW = 44.65kW Maximum resistance value: Multiply the nominal value by the tolerance and then add this to the nominal value: nominal value + nominal value * tolerance 47k  47k * 0.05 47k  2.35k 49.35k 5-Band Resistors For resistors with 1% or 2% tolerance, the color code consists of 5 bands. The template for 5-band resistors is: 1st Band = 2nd Band = 3rd Band = 4th Band = 5th Band = 1st Significant 2nd Significant 3rd Significant Multiplier Tolerance Digit Digit Digit ___ ___ ___  10    ____ % Example 4. Determine the nominal resistance and tolerance for the resistor shown below. Solution: Brown = 1 Black =0 Black = 0 Brown = 1 Red =  2% 1 1 ___ 0 ___0 ___  10    ____2% Resistor nominal value = 100101 = 1,000 = 1k. Tolerance = 2% Which side of a resistor do I read from? A question that often arises when reading the color code of real resistors is: how do I determine which side of a resistor do I read from? Answer: For 4-band resistors a gold or silver band is always the last band. If the resistor has 5 bands or if there is no tolerance band (20%), then the first band is the one located closest to a lead.  Capacita Capacitance is the ability of a device to store nce electrical energy in an electrostatic field. A capacitor is a device that stores energy in the form of an electrical field.. A capacitor is made of two conductors separated by a dielectric. S.I Unit: Farad (F) Symbol: C Two important Properties: 1. No current flows through the capacitor, if the voltage remains constant. 2. Voltage across a capacitor cannot change instantaneously.  Inductan ce Inductance is the characteristic of an electrical conductor that opposes a change in current flow. An inductor is a device that stores energy in a magnetic Whenfield.a current flows through a magnetic field builds up around the conductor, field contains conductor. This energy and is the foundation for inductance. S.I Unit: Henry (H) Symbol: L Two important Properties: 1. No voltage appears across an inductor, if the current through it remains constant. 2. The current through an inductor cannot change instantaneously.  Capacitance and Inductance 𝑄 𝑉 = 𝐿 = 𝐶𝑉 𝑑 L: Inductance (Henry) 𝐼 = 𝐶𝑉 = 𝑑𝑄 𝑑 𝑑𝑉 𝑑𝐼 𝐸 = 1𝑡 2 u: Permeability of the 𝑑𝑡 𝑑𝑡 = 1 2 𝐶 𝑑𝑡 material (Henry/meter) 2 𝐸 𝐿𝐼 𝜇 𝑁2 N: Number of turns in a coil 𝐿 𝐴 A: Cross-sectional area of 2 = 𝐶𝑉 𝗅(length of coil) the coil (meter^2) 𝐶 = l: Length of the coil (meter) = 𝐴∈ ε (epsilon) is the permittivity of the material between the plates of the capacitor. It is a measure of how easily an electric field can be established in the material. Permittivity is measured in Farads per meter (F/m).  Active devices can also be used as_________ a) Amplifiers b) Choppers c) Converters d) Inverters  Series SERIES Connection CONNECTION: Two or more elements are in series if they exclusively share a single node and consequently carry the same current. Point to Remember for Series Circuits  Parallel Connection PARALLEL CONNECTION: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them Battery Voltage In Series And Parallel Note: Resistors in series behave as a single resistor whose resistance is equal to the sum of the resistances of the individual resistors. Resistors in Parallel. How to find Equivalent Resistance for Series- Parallel Combinations find 𝑹𝒆𝒒 Example: To  HW QUICK QUIZ (Poll 1) 1 Coulomb is same as: A. Watt /sec B. Ampere/sec C. Joule-sec D. Ampere-sec  QUICK QUIZ The total charge entering the terminal is 5𝑠𝑖𝑛4𝜋𝑡 𝑚𝐶. (Poll 2) Calculate current at t= 0.5 sec.: A. 31.2 A B. 31.2 mA C. 62.8 mA D. 62.8 A  QUICK QUIZ (Poll 3) Calculate the current ratings of 100 Watt incandescent bulb and 15 Watt LED lamp operated with the domestic supply of 220 Volt? A. Bulb = 0.068 A and LED = 0.45 A B. Bulb = 0.45 A and LED = 0.068 A C. Bulb =0.50 A and LED = 0.068 A D. Bulb = 0.50 and LED = 0.68 A  QUICK QUIZ (Poll 4) From the previous question, it can be inferred that: A. LED consumes 5 times more current than Bulb. B. Bulb consumes 5 times more current than LED.. C. LED consumes 6.6 times more current than Bulb. D. Bulb consumes 6.6 times more current than LED.  QUICK QUIZ (Poll 5) Identify the passive element A. Battery B. Transformer C. Transistor D. OP-amp  QUICK QUIZ (Poll 6) Find the value of capacitance if the value of voltage increases linearly from 0 to 100 V in 0.1 s causing a current flow of 5 mA? A. 10 µF B. 5 F C. 10 F D. 5 µF  QUICK QUIZ (Poll 7) Find Equivalent Resistance in Ohms? A. 5 B. 10 C. 15 D. 20  QUICK QUIZ (Poll 8) Find Equivalent Resistance in Ohms? A. 12 B. 17 C. 19 D. 29