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ELECTRIC CIRCUIT ANALYSIS

Dr.P.Vidhyalakshmi

Assistant Professor(SLG)

Department of EIE

Kongu Engineering College

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(i) 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, R
The mathematical equation that describes this relationship is:

V=IR�

basic laws

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(ii) Kirchhoff’s current law

Kirchhoff's Current Law (KCL) : 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) or, in other words, the sum of all currents entering & leaving a node is equal to zero.

The current entering any junction is equal to the current leaving that junction. i₁ + i₄ = i₂ + i₃

This law is also called Kirchhoff's first law, Kirchhoff's point rule, Kirchhoff's junction rule, and Kirchhoff's first rule.

A node

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(ii) Kirchhoff’s voltage law

Kirchhoff's Voltage Law (KVL): 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 or, in other words the sum of all the voltages around a single closed loop is zero.

also called Kirchhoff's second law, Kirchhoff's loop(or mesh) rule, and Kirchhoff's second rule.
V_s=V₁+V₂+V₃+…+V_n

Vs+V₁+V₂+V₃+…V_n=0

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Simple DC circuits

DC circuit is an electrical circuit that consists of any combination of constant voltage sources, constant current sources, and resistors.
Two basic circuits:

i. Series Circuit - Components are connected end-to-end so there is only one path for the current to flow.

ii. Parallel Circuit - Components are connected side-by-side so there are multiple paths for the current to flow.

Series Circuit

Parallel Circuit

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Series circuits:

Use Ohm’s Law across each resistor

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Parallel circuit

Use Ohm’s Law to calculate currents

Only for 2 R

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Series circuit vs Parallel circuit

Electrical unit	Series circuit	Parallel circuit
Current	I=I₁=I₂=I₃	I=I₁+I₂+I₃
Voltage	V=V₁+V₂+V₃	V=V₁=V₂=V₃
Resistance	R_T=R₁+R₂+R₃	1/R_T=1/R₁+1/R₂+1/R₃

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Voltage division principles �

A series circuit acts as a voltage divider
Consider single loop circuit with two resistors in series. Applying Ohm’s and KVL’s laws, we obtain:

V_s

R₁

R₂

V₁

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Current division principle

A parallel circuit acts as a current divider because current entering the junction of parallel branches “divides” up into several individual branch currents

Consider single loop circuit with two resistors in parallel.

Applying Ohm’s and KCL’s laws, we obtain:

R₂

R₁

V_s

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Delta to Star conversions

Each resistor to the star is equal to the product of resistors in two adjacent delta branches, divided by the sum of all three delta resistors.

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Star to delta conversions

Each resistor in the delta is equal to the sum of all possible products of wye resistors taken two at a time, divide by the opposite star resistor.

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