Electrical circuits lecture 1b

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Dr inż. Agnieszka Wardzińska Room: 105 Polanka agnieszka.wardzinska@put.poznan.pl cygnus.et.put.poznan.pl/~award Advisor hours: Tuesday: 10.00-10.45 Thursday: 10.30-11.15

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Impedance of AC components

 Impedance Z compose of resistance R and reactance X.

 _{The inverse of impedance is admitance Y .}

 Admitance has real part conductance G and

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-Impedance of AC components

 Note:

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-Ohms Law

For the DC

For the AC

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AC capacitor circuits

Real capacitor

Quality factor (Q factor)

. . .

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AC inductor circuits

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AC inductor circuits

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AC inductor circuits

Real inductor

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Circuit Elements Ideal

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Circuit Elements Ideal

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Circuit Elements – dependent sources  Ideal dependent voltage source  Ideal dependent current source

The voltage defined by the source depends on the

voltage or current

determined in this or other circuit

The current defined by the source depends on the

voltage or current

determined in this or other circuit

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The real voltage sources

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The real current sources

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Ideal Wires

 we will assume that an ideal wire has zero total resistance, no capacitance, and no inductance.

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Kirchhoff’s Circuit Laws

 Kirchhoff’s circuit laws were first described in 1845 by Gustav Kirchhoff. They consist from two equalities for the lumped element model of electrical circuits. They describe the current and voltage behaviour in the

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Kirchhoff’s First Law - Kirchhoff’s Current Law (KCL)

 The algebraic sum of currents in a network of conductors meeting at a node is zero.

It can be described by the equation:

The currents flowing into the node (I1, I6) we describe as positive, the currents flowing outthe node (I2, I3, I4, I5) we describe as negative.

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Kirchhoff’s Second Law

-Kirchhoff’s Voltage Law (KVL)

 The algebraic sum of the potential rises and drops around a closed loop or path is zero.

where U_i describes both the potential drops at the elements and the

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Series Connection

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 Voltage drops add to total voltage.

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Ohm’s Law

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Ohm’s Law

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Ohm’s Law

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Ohm’s Law

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Ohm’s Law

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Ohm’s Law

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Parallel Connection

 All components are conected between the same two sets of electrically common points.

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 All components are conected between the same two sets of electrically common points.

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 Currents add to total current.

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 Currents add to total current.

 Voltage drop on the components are the same. u

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Parallel Connection u

Ohm’s Law

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Ohm’s Law

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Ohm’s Law

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Ohm’s Law

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Ohm’s Law

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Series-Parallel Connection

Z1 – series – Z2 Z3 – series – Z4 Z1+Z2 parallel to Z3+Z4 parallel to Z5 Z1 Z3 Z2 Z4 Z5

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Delta-Y conversions

 the Δ, spelled out as delta, can also be called triangle, Π (spelled out as pi), or mesh

Z_AB Z_AB

Z_BC Z_CA

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Delta-Y conversions

 The Y, spelled out as wye, can also be called T or star

Z_C

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Delta-Y conversions

From Wye (Y) to Delta 

Z_C

Z_AB

Z_BC Z_CA

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Delta-Y conversions From Delta  to Wye (Y)

Z_C

Z_AB

Z_BC Z_CA