Impedance Triangle | What Is Impedance Triangle

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Impedance Triangle | What Is Impedance Triangle

 

Impedance Triangle | What Is Impedance Triangle :- The triangle drawn to graphically represent the effects of resistance, inductance, and capacitance in an AC circuit is called the impedance triangle. This triangle is used to show the relationship between voltage and current and helps in understanding the impedance of the circuit.

Impedance Triangle | What Is Impedance Triangle - Curio Physics

Components of the impedance triangle :

  • Resistance (R) : The resistance of the circuit is represented by the base of the impedance triangle.
  • Total Reactance (X) : The total reactance of the circuit is represented by the perpendicular of the triangle. The length of this perpendicular is equal to the difference between the inductive reactance (XL) and the capacitive reactance (XC).
  • Impedance (Z) : The impedance of the circuit is represented by the hypotenuse of the triangle. The length of the hypotenuse is determined from R and X using the Pythagorean theorem.

Calculation of impedance from Impedance Triangle :

From the Pythagorean theorem,

\displaystyle Z=\sqrt{{{R}^{2}}+{{\left( {{X}_{L}}-{{X}_{C}} \right)}^{2}}}

The impedance triangle is used to understand the phase angle between voltage and current in an AC circuit, and it helps in calculating the total impedance of the entire circuit.

Phase angle between the resultant voltage and current (Φ) :

\displaystyle tan\phi =\frac{{{X}_{L}}-{{X}_{C}}}{R}

Note :-

(1). The reciprocal of reactance is called susceptance .

Inductive Susceptance) (SL) :

\displaystyle {{S}_{L}}=\frac{1}{{{X}_{L}}}=\frac{1}{\omega L}

Capacitive susceptance (SC) :

\displaystyle {{S}_{\text{C}}}=\frac{1}{{{X}_{C}}}=\omega C

(2). The reciprocal of impedance is called admittance .

\displaystyle Y=\frac{1}{Z}=\frac{1}{\sqrt{{{R}^{2}}+{{\left( {{X}_{L}}-{{X}_{C}} \right)}^{2}}}}

(3). The susceptance and the admittance both have the SI unit mho or ohm-1 (Ω-1), also known as the Siemen.

 

 

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