Circuits 2
Chapter 2: Impedance and Admittance
PHASOR RELATIONSHIPS FOR CIRCUIT ELEMENT
Summary of Voltage Current Relationships
IMPEDANCE AND ADMITTANCE
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The impedance Z of a circuit is the ratio of the phasor voltage V to the phasor current I,
measured in ohms Ω.
The impedance represents the opposition which the circuit exhibits to the flow of
sinusoidal current.
It is not a phasor
Impedances and Admittances of Passive Elements
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The impedance may be expressed in rectangular form a
𝑍 = 𝑅 + 𝑗𝑋
where:
R = Re Z (resistance )
X = Im Z (reactance).
The reactance X may be positive or negative.
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Circuits 2
Chapter 2: Impedance and Admittance
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the impedance is inductive when X is positive or capacitive when X is negative. T
impedance Z = R + jX is said to be inductive or lagging since current lags voltage,
impedance Z = R − jX is capacitive or leading because current leads voltage.
The impedance, resistance, and reactance are all measured in ohms.
The impedance may also be expressed in polar form as
Admittance
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The Reciprocal of Impedance
The admittance Y of an element (or a circuit) is the ratio of the phasor current through it
to the phasor voltage across it, or
Complex Form of Admittance:
𝑌 = 𝐺 ± 𝑗𝛽
where
G = Re Y (the conductance)
β = Im Y is called the susceptance.
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Admittance, conductance, and susceptance are all expressed in the unit of siemens (or
mhos).
Examples:
1. What is the inductance of the inductor in millihenrys
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Circuits 2
Chapter 2: Impedance and Admittance
2. Simplify:
a. 𝑓(𝑡) = 5 cos(2𝑡 + 15°) − 4sin⁡(2𝑡 − 30°)
b. 𝑔(𝑡) = 8𝑠𝑖𝑛𝑡 + 4cos⁡(𝑡 + 50°)
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Circuits 2
Chapter 2: Impedance and Admittance
3. The voltage v= 12 cos(60t + 45◦) is applied to a 0.1-H inductor. Find the steady-state
current through the inductor.
4. Determine the current that flows through an 8-Ω resistor connected to a voltage source
𝑣𝑠 = 110 cos 377𝑡⁡𝑉.
5. What is the instantaneous voltage across a 2- µ F capacitor when the current through it
is 𝑖 = 4 sin(106 + 25°) 𝐴
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Circuits 2
Chapter 2: Impedance and Admittance
6. A voltage 𝑣(𝑡) = 100 cos(60𝑡 + 20°) 𝑉 is applied to a parallel combination of a 40-kΩ
resistor and a 50- µ F capacitor. Find the steady-state currents through the resistor and
the capacitor.
7. Find v(t) and i(t) in the circuit shown:
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Circuits 2
Chapter 2: Impedance and Admittance
8. The phasor form of voltage applied across the inductor is, V=100∠0∘V The phasor form
of current in the inductor is, I=20∠-90∘A. Determining the impedance of the inductor:
9. Two voltages 𝑣1 and 𝑣2 appear in series so that their sum is v = v1 + v2. If v1 = 10
cos(50t - π/3)V and v2 = 12cos(50t + 30° ) V, find v.
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Circuits 2
Chapter 2: Impedance and Admittance
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