Basic Electrical Circuits
Basic Electrical Laws
Mehedi Hasan Masud
Lecturer, Dept. of EEE
Dhaka International University
Ohm’s Law
Ohm’s law states that the voltage v across a resistor is directly proportional to the
current i flowing through the resistor.
𝑣∝𝑖
𝑣 = 𝑖𝑅
R = Resistance
𝑙
𝑅=𝜌
𝐴
𝜌 = Resistivity of the material
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Ohm’s Law
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Nodes, Branches, and Loops
1. A branch represents a single element such as a voltage source or a resistor.
2. A node is the point of connection between two or more branches.
3. A loop is any closed path in a circuit.
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Kirchhoff’s Current Law
Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a
node (or a closed boundary) is zero.
Mathematically, KCL implies that,
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Kirchhoff’s Voltage Law
Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around
a closed path(or loop) is zero.
Mathematically, KCL implies that,
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Practice Problem
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Practice Problem
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Series Resistor & Voltage Division
The equivalent resistance of any number of resistors connected in series is the sum
of the individual resistances.
For N resistors in series then,
the nth resistor (Rn) will have a voltage drop of,
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Parallel Resistor & Current Division
The equivalent resistance of two parallel resistors is equal to the product of their
resistances divided by their sum.
For N resistors in parallel then,
the nth resistor (Rn) will have a current,
𝑖𝑛 =
𝑅𝑁 −1
𝑅1
−1
+ 𝑅2
−1
+ … … . . +𝑅𝑁
−1
×𝑖
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Practice Problem
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Practice Problem
Aminul Islam Munna
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Wye – Delta & Delta – Wye Conversion
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Wye – Delta & Delta – Wye Conversion
Wye - Delta
𝑅12
1
2
𝑅23
𝑅13
𝑅1 × 𝑅2
= 𝑅1 + 𝑅2 +
𝑅3
𝑅2 × 𝑅3
= 𝑅2 + 𝑅3 +
𝑅1
𝑅1 × 𝑅3
= 𝑅1 + 𝑅3 +
𝑅2
Delta - Wye
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𝑅12 × 𝑅13
𝑅1 =
𝑅12 + 𝑅23 + 𝑅13
𝑅12 × 𝑅23
𝑅2 =
𝑅12 + 𝑅23 + 𝑅13
𝑅13 × 𝑅23
𝑅3 =
𝑅12 + 𝑅23 + 𝑅13
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Practice Problem
Aminul Islam Munna
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Nodal Analysis
Current flows from a higher potential to a lower potential in a resistor.
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Practice Problem
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Practice Problem
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Mesh Analysis
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Practice Problem
Aminul Islam Munna
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Practice Problem
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