One time: Test: Impedence - Electrical Engineering (EE) MCQ

Concept:

The load impedance is given by:

Z = R + j X (for lagging load)

Z = R - j X (for leading load)

The power factor is given by:

Calculation:

Given, Z = 20 - j20

cosϕ = 0.707 leading

Impedance:

Concept:

The impedance of the coil is given by:

Z = R + jX_L

where Z = impedance

R = resistance

X_L = inductive reactance

The magnitude of 'Z' is given by:

 Z² =  R² + X_L²

Calculation:

Given, Z = 25Ω 

R = 15Ω 

X_L² = Z² - R²

X_L² = 25² - 15²

X_L² = 400

X_L = √400

X_L = 20Ω 

Concept:

Impedance:

• It is the measure of the opposition that a circuit presents to a current when a voltage is applied.
• It is the ratio of Voltage to Current.
• Impedance is a complex number, with the same units as resistance, for which the SI unit is the ohm (Ω).
• Its symbol is usually Z, and it may be represented by writing its magnitude and phase in the polar form |Z|∠θ.

Admittance:

• Admittance is a measure of how easily a circuit or device will allow a current to flow.
• It is defined as the reciprocal of impedance, analogous to how conductance & resistance are defined.
• The SI unit of admittance is the siemens (symbol S or  ℧(mho)).
• It is denoted as Y, and it may be represented by writing its magnitude and phase in the polar form |Y|∠θ.

Calculation:

Given

V = 100.0 ∠45° V  and I = 5.0 ∠15° A

Concept:

Inductive Reactance (XL) = jωL

Capacitive Reactance (XC) = 1 / jωC

Application:

According to the above concept, the given circuit can be modified as,

Hence,

Z_in = (-j10) + [(3 - j2)||(8 + j10)]

or, 

or, Z_in = (3.22 - j 11.07) Ω

The relationship between the impedance and admittance is given by:

Z = 1/Y

where Z = Impedance

Y = Admittance

The impedance is analogous to admittance in the following ways:

Resistance

It is an electrical parameter that is used as the measurement of opposition to the electric current.

The reciprocal of the resistance is called the 'Admittance'.

Resistance is defined as:

R = ρl/A

ρ: Resistivity of the material

l: length of the conductor

A: Area of the cross-section of the conductor.

It is measured in Ω.

Impedance:

The complex quantity of the resistance is defined as the Impedance of a circuit. 

It is the same as that of the resistance.

Admittance

It is defined as the parameter which is used to measure the flow of current easily in a circuit.

admitatance = 1/resistance

It is measured in Ω-1 or Siemens(S).

From Ohm's law admittance is:

Admittance = I/V

Capacitance

It is an electrical element that stores energy in the form of a static electric charge.

Energy stored in a capacitor is:

E = 1/2CV²

V: Voltage across the capacitor.

SI unit is Farads. (F)

Concept:

For a series RLC circuit, the net impedance is given by:

R = Resistance

X_L = Inductive reactance

X_C ­= Capacitive reactance

Net reactance of the circuit is given by

X = |X_L – X_C|

Calculation:

Given that,

R = 20 Ohms, X_L = 30 Ohms and X_C = 10 Ohms

The net reactance of the circuit will be:

X = |30 - 10|

X = 20 Ω

Concept:

Properties of RC network:

• Poles and zeroes are simple, lies only on the -ve real axis of the s-plane.
• Poles and zeroes should be alternate.
• The first critical frequency should be a pole and the pole can be at origin (s = 0)
• The last critical frequency should be a zero and zero can be at s = ∞ 

Properties of RL Network:

• Poles and zeroes are simple, lies only on the -ve real axis of the s-plane.
• Poles and zeroes should be alternate
• The first critical frequency should be zero and this can be at the origin (5 = 0)
• The lost critical frequency should be a pole and this can be at s = ∞ 

Properties of the LC network:

• Poles and zeroes will be complex and lie on the imaginary axis of the s-plane.
• Poles and zeroes will be alternate.

Analysis:

Given function is:

The pole-zero plot is given below:

If we compare with the above 3 pole-zero plots, none of them are matching. So, the given driving point impedance belongs to the R-L-C network.

Concept:

In a series RLC circuit, the impedance is given by

R is resistance

X­_L is inductive reactance = ωL

X_C is capacitive reactance = -1/ωC

(X_L – X_C) is net reactance

At the resonant frequency, inductive reactance is equal to capacitive reactance i.e. X_L = X_C

So, at this condition the impedance is minimum, and it is equivalent to R.

Explanation:

Given that, resistance (R) = 5 Ω

Capacitive reactance (X_C) = 20 Ω

Inductive reactance (X_L) = 12 Ω

Net Impedance Z is calculated as:

In parallel circuits, the current across the circuits vary whereas the voltage remains the same. So, current in each impedance is different.

In a parallel circuit, we consider admittance instead of impedance, where admittance is the reciprocal of impedance.

Although slotted lines used to be the principal way of measuring unknown impedance at microwave frequencies, they have largely been superseded by the modern network analyzer in terms of accuracy, versatility and convenience.

Impidance diagram is made for the analysis of load flow. Fault analysis is doen by the help of reactance diagram. All these diagrams are made using symmetrical component analysis method on per phase basis.

Almost all electric circuits offer impedance to the flow of current. Impedance is a complex quantity having the real part as resistance and the imaginary part as reactance.