Linear Circuit Analysis: Key Formulas for Resistors, Capacitors, and More


Essential Circuit Analysis Formulas

⚡ Essential Circuit Analysis Formulas⚡

📌 Basic Electrical Formulas

CategoryFormulaNotes
Ohm’s LawV = IRRelates voltage, current, and resistance
Power FormulaP = VI = I²R = V²/RDifferent power forms using Ohm’s law

🔥 Resistors & Capacitors

CategoryFormulaNotes
Resistors in SeriesReq = R1 + R2 + …Total resistance adds up
Resistors in Parallel1/Req = 1/R1 + 1/R2 + …Reciprocal sum for parallel resistance
Capacitors in Series1/Ceq = 1/C1 + 1/C2 + …Opposite of resistors
Capacitors in ParallelCeq = C1 + C2 + …Direct sum for parallel capacitors

⚙️ Inductor Formulas

CategoryFormulaNotes
Inductors in SeriesLeq = L1 + L2 + …Same as resistors in series
Inductors in Parallel1/Leq = 1/L1 + 1/L2 + …Same as resistors in parallel
Energy Stored in InductorW = (1/2) L i²Energy stored in a magnetic field
RL Time Constantτ = L/RTime constant for inductor current change

⚡ Voltage & Current Divider Rules

CategoryFormulaNotes
Voltage Divider Rule (VDR)Vx = Vtotal × (Rx / Rtotal)Used when resistors are in series
Current Divider Rule (CDR)Ix = Itotal × (Rother / Rtotal)Used when resistors are in parallel

🌀 Formulas

CategoryFormulaNotes
RC Charging VoltagevC(t) = Vf(1 - e-t/τ)Exponential capacitor charging
RC Discharging VoltagevC(t) = V0 e-t/τExponential capacitor discharging
RL Current ResponseiL(t) = i0 e-t/τInductor current decay

⚡ Step Response Formulas (RC & RL Circuits)

📌 For Capacitors in RC Circuits:

CategoryFormulaNotes
RC Charging Voltage vC(t) = Vf + (V0 - Vf) e-t/τ General capacitor voltage formula
Special Case (Uncharged Capacitor Charging) vC(t) = Vs (1 - e-t/τ) When V0 = 0, capacitor starts from 0V
RC Discharging Voltage vC(t) = V0 e-t/τ When capacitor discharges, Vf = 0
RC Time Constant τ = RC Time for voltage to reach ~63% of Vf

⚡ For Inductors in RL Circuits:

CategoryFormulaNotes
RL Current Response iL(t) = If + (I0 - If) e-t/τ General inductor current response
Special Case (Inductor Starting from 0A) iL(t) = Is (1 - e-t/τ) When I0 = 0, inductor builds current
RL Discharging (Decay of Inductor Current) iL(t) = I0 e-t/τ Inductor current decreases over time
RL Time Constant τ = L/R Time for current to reach ~63% of If

🔗 Thevenin & Norton Equivalents

CategoryFormulaNotes
Thevenin VoltageVth = Vopen-circuitVoltage seen at terminals when load is removed
Norton CurrentIN = Vth / RthCurrent when terminals are shorted

🔎 Circuit Analysis Techniques

TechniqueDescription
Superposition TheoremSolve circuit by considering one source at a time
Nodal AnalysisUses KCL and node voltages to solve circuits
SupernodeUsed when voltage sources connect two nodes
Mesh AnalysisUses KVL and mesh currents to solve circuits
SupermeshUsed when a current source exists between two meshes

🔍 (For Nerds)

T2ggbWFuLCBOSUNFLCB5b3UgdHJpZWQgdG8gZGVjb2RlIG1lISBHcmVhdCB3b3JrIGJ0dy4uLg==

📢 Disclaimer

Help provided as a courtesy. Outcomes and decisions are yours to own.
AI has been used to assist in creating this content. If any errors are found, please contact Bilal Ahmad Khan AKA Mr. BILRED ASAP.

GitHub: I have uploaded some other subject notes on my GitHub profile, mostly in PDF form. Feel free to visit.
🔗 My GitHub

What I Think:
"Knowledge Should Be Shared Only With The One Who Knows Its True Worth! Not Everyone Deserves It."
- Bilal Ahmad Khan AKA Mr. BILRED

Comments

Post a Comment

Popular posts from this blog

C++ Arrays Explained: Syntax, Examples & Theory | Compiled By Bilal Ahmad Khan AKA Mr. BILRED | CppNotes

Image
Arrays in C++ – Easy Explanation with Examples Understanding Arrays in C++ – Easy Guide for Beginners By Bilal Ahmad Khan AKA Mr. BILRED Asking Positively! Have you ever wondered WHY SHOULD WE EVEN USE ARRAYS? Like, WHY? Look Arrays help programmers store and manage multiple values efficiently. This guide explains arrays in C++ with simple examples. 📌 What is an Array in C++? An array is a collection of similar data types stored in a single variable. Instead of creating multiple variables, an array lets us store multiple values in one place. In "mere walay alfaaz", Agar aap chaahty ho aap ziada saari values store karo, to kia phir har dafa variables define karty raho gy? NAHI Na! Phir isko solve karna he arrays k zariye! But first, understand its basic syntax Basic SYNTAX Of Arrays data_type array_name[size]; ✅ Example: int numbers[5] = {10, 20, 30, 40, 50}; cout 📌 Importance; Why Do We Use Arrays? 🔹 Saves Space: No need to create separat...
Read more

Comparison of Key Electromagnetic & Newtonian Laws - Compiled By BILRED

Image
  Comparison of Key Electromagnetic & Newtonian Laws Law/Effect Formula/Equation Key Variables & Meaning What It Describes/Applies To Similarities/Differences Coulomb’s Law  (Electric Force) F = k q 1 q 2 r 2 -  F : Electric force (N) -  k : Coulomb constant  9 × 10 9  Nm²/C² -  q 1 , q 2 : Charges (C) -  r : Distance (m) Describes the force between two point charges. Similar to Newton’s gravitational law but for electrostatics. Inverse Square Law:  Like gravity but for electric charges. Electric Field ( E ) E = F q = k Q r 2 -  E : Electric field (N/C) -  Q : Source charge (C) -  r : Distance (m) Defines the field created by a charge and the force it exerts on another charge. Like gravitational field ( g ) , but for electric forces. Gauss’s Law (Electric Fields) ∮ E ⋅ d A = Q enc ε 0 -  E : Electric field (N/C) -  d A : Surface area element (m²) -  Q enc : Enclosed charge (C) Relates the total electric f...
Read more