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Fundamentals of Electric Circuits: Ohm's Law, Kirchhoff's Laws, and Circuit Analysis, Lecture notes of Electrical Circuit Analysis

A concise introduction to the fundamental laws governing electric circuits, including ohm's law, kirchhoff's voltage law (kvl), and kirchhoff's current law (kcl). It explains the relationship between voltage, current, and resistance, and demonstrates how these laws can be applied to analyze and design circuits. The document also highlights the connection between these laws and fundamental physical conservation principles, such as conservation of energy and charge.

Typology: Lecture notes

2017/2018

Available from 01/21/2025

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ELECTRIC CIRCUITS: BASICS OF VOLTAGE AND CURRENT LAWS
- Electric circuits follow fundamental principles described by Ohm's Law, Kirchhoff's Voltage
Law (KVL), and Kirchhoff's Current Law (KCL). These laws help analyze and design circuits
by describing the behavior of voltage, current, and resistance.
1. Ohm's Law
Ohm's Law is the foundation for understanding electric circuits. It relates voltage (V), current (I), and
resistance (R):
V=IR
Key Points:
V: Voltage (in volts, V)—the energy per unit charge driving the current.
I: Current (in amperes, A)—the flow rate of electric charge.
R: Resistance (in ohms, Ω)—the opposition to the flow of current.
2. Kirchhoff's Voltage Law (KVL)
KVL states that the sum of all voltages around any closed loop in a circuit is zero:
∑V=0
Explanation:
The total energy gained by charges from voltage sources equals the energy lost in resistive
components.
Voltage drops (−V) are subtracted, while voltage rises (+V) are added.
Application Example:
For a simple loop with a voltage source Vs, a resistor R, and a capacitor C:Vs−IR−VC=0
3. Kirchhoff's Current Law (KCL)
KCL states that the total current entering a junction equals the total current leaving it:
∑Iin=∑Iout
Explanation:
At any node (junction), the incoming current is distributed among the outgoing branches.
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ELECTRIC CIRCUITS: BASICS OF VOLTAGE AND CURRENT LAWS

  • Electric circuits follow fundamental principles described by Ohm's Law , Kirchhoff's Voltage Law (KVL) , and Kirchhoff's Current Law (KCL). These laws help analyze and design circuits by describing the behavior of voltage, current, and resistance. 1. Ohm's Law Ohm's Law is the foundation for understanding electric circuits. It relates voltage (V), current (I), and resistance (R): V=I⋅R Key Points:  V: Voltage (in volts, V)—the energy per unit charge driving the current.  I: Current (in amperes, A)—the flow rate of electric charge.  R: Resistance (in ohms, Ω)—the opposition to the flow of current. 2. Kirchhoff's Voltage Law (KVL) KVL states that the sum of all voltages around any closed loop in a circuit is zero: ∑V= Explanation:  The total energy gained by charges from voltage sources equals the energy lost in resistive components.  Voltage drops (−V) are subtracted, while voltage rises (+V) are added. Application Example:

For a simple loop with a voltage source Vs, a resistor R, and a capacitor C:Vs−IR−VC=

3. Kirchhoff's Current Law (KCL) KCL states that the total current entering a junction equals the total current leaving it: ∑Iin=∑Iout Explanation:  At any node (junction), the incoming current is distributed among the outgoing branches.

Application Example: For a node with three branches:  Incoming current: I  Outgoing currents: I2 and I I1=I2+I

4. Combining KVL and KCL Using KVL and KCL together enables solving complex circuits, including those with multiple loops and nodes. These laws form the basis of circuit analysis techniques like:  Node Voltage Analysis : Solves for voltages at nodes using KCL.  Mesh Current Analysis : Solves for currents in loops using KVL. 5. Conservation Laws Both KVL and KCL are rooted in physical conservation laws:  KVL is based on the conservation of energy.  KCL is based on the conservation of charge.