Equivalent Impedance MCQ Quiz - Objective Question with Answer for Equivalent Impedance - Download Free PDF
Last updated on Apr 19, 2025
Latest Equivalent Impedance MCQ Objective Questions
Equivalent Impedance Question 1:
In an LCR series circuit, source of emf is:
E = 30 sin (100t) and R = 120 Ω, L = 100 mH, C = 100 µF
(A) The numerical value of impedance
(B) The numerical value of Resistance R
(C) The numerical value of capacitive reactance
(D) The numerical value of inductive reactance
Arrange the values of quantities mentioned in (A, B, C, D) in increasing order.
Answer (Detailed Solution Below)
Equivalent Impedance Question 1 Detailed Solution
The correct answer is - (D), (C), (B), (A)
Key Points
- Impedance (Z)
- For an LCR series circuit, the impedance Z is given by the formula: Z = √(R² + (XL - XC)²).
- Here, R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.
- Resistance (R)
- The resistance R is given directly as 120 Ω.
- Inductive Reactance (XL)
- The inductive reactance XL is given by the formula: XL = ωL, where ω is the angular frequency (100 rad/s) and L is the inductance.
- Using the values: XL = 100 × 100 × 10-3 = 10 Ω.
- Capacitive Reactance (XC)
- The capacitive reactance XC is given by the formula: XC = 1 / (ωC), where ω is the angular frequency (100 rad/s) and C is the capacitance.
- Using the values: XC = 1 / (100 × 100 × 10-6) = 100 Ω.
Additional Information
- Impedance Calculation
- Using the values calculated above, we have: Z = √(120² + (10 - 100)²) = √(120² + (-90)²) = √(14400 + 8100) = √22500 = 150 Ω.
- Order of Values
- From the values calculated, we get the following numerical order:
- XL = 10 Ω
- R = 120 Ω
- XC = 100 Ω
- Z = 150 Ω
- From the values calculated, we get the following numerical order:
Equivalent Impedance Question 2:
Calculate the value of Norton's current and Norton's equivalent resistance for the given circuit across the terminal AB.
Answer (Detailed Solution Below)
Equivalent Impedance Question 2 Detailed Solution
Norton's Theorem :
Any linear bilateral network consisting of multiple resistances and sources can be replaced by a resistor RN in parallel of Current source IN .
Calculation:
RN :
Disable all independent sources and find equivalent resistance.
RN = ( 20 || 10 ) + 20 = 26.6 ohm
IN :
Short circuited current
Let node voltage of 10 ohm is V
Apply nodal analysis
V = 2.5V
IN = V /20 = 125 mA
Equivalent Impedance Question 3:
A 120 V, 20 Hz source supplies a series circuit consisting of a 5 Ω capacitive reactance, a 1.6 Ω resistor, and a coil with resistance and inductive reactance of 3 Ω and 1.2 Ω respectively.
(i) The input impedance is Z
(ii) The circuit current is I
(iii) The voltage across the coil is VL
(iv) The resonant frequency fr
Arrange the above in increasing order of their numerical values.
Answer (Detailed Solution Below)
Equivalent Impedance Question 3 Detailed Solution
Req = 3 + 1.6 = 4.6 Ω
(i). The input impedance is Z
Z = 5.96
(ii) Circuit Current
(iii) Voltage across the coil is,
VL = 64.97 ∠ -61.36 °
(iv) Resonant frequency is given as,
Xl = 1.2 (f = 20 Hz)
2π fL = 1.2
Xc = 1 / (2πfC) = 5
fr = 40.82 Hz
Hence correct order is,
Z L
i
Equivalent Impedance Question 4:
Identify the type / status of circuit the below diagram represents.
Answer (Detailed Solution Below)
Equivalent Impedance Question 4 Detailed Solution
Concept:
Case I:
Series RLC load with inductive reactance more than the capacitive reactance implies it is equivalent to a series RL circuit.
Here, current lags voltage as shown
Case II:
Series RLC load with inductive reactance lesser than the capacitive reactance implies it is equivalent to a series RC circuit.
Here, current leads voltage as shown
Where,
VL = Inductor voltage
VC = Capacitor voltage
I = Current
V = Supply voltage
VR = Resistor Voltage
Application:
Given Circuit:
R = 6Ω, XL = j8, Xc = - j10
Zeq = (6 + j8) ∥ (- j10)
= 15 - j5 Ω
Net current from the supply is given by
Current is leading with respect to Voltage by 18.43∘
Therefore,
This indicates RC circuit
Equivalent Impedance Question 5:
In the following circuit, input impedance Zin(s) is ______
Answer (Detailed Solution Below)
Equivalent Impedance Question 5 Detailed Solution
Applying KCL at the node A in the Laplace domain, we get
Ix = 50 × 10-3 sVx(s) + 5 × 10-3s Vx(s) - 50 × 10-3s Vx(s)
Ix = sVx(s) [5 × 10-3]
Top Equivalent Impedance MCQ Objective Questions
Identify the type / status of circuit the below diagram represents.
Answer (Detailed Solution Below)
Equivalent Impedance Question 6 Detailed Solution
Download Solution PDFConcept:
Case I:
Series RLC load with inductive reactance more than the capacitive reactance implies it is equivalent to a series RL circuit.
Here, current lags voltage as shown
Case II:
Series RLC load with inductive reactance lesser than the capacitive reactance implies it is equivalent to a series RC circuit.
Here, current leads voltage as shown
Where,
VL = Inductor voltage
VC = Capacitor voltage
I = Current
V = Supply voltage
VR = Resistor Voltage
Application:
Given Circuit:
R = 6Ω, XL = j8, Xc = - j10
Zeq = (6 + j8) ∥ (- j10)
= 15 - j5 Ω
Net current from the supply is given by
Current is leading with respect to Voltage by 18.43∘
Therefore,
This indicates RC circuit
A 120 V, 20 Hz source supplies a series circuit consisting of a 5 Ω capacitive reactance, a 1.6 Ω resistor, and a coil with resistance and inductive reactance of 3 Ω and 1.2 Ω respectively.
(i) The input impedance is Z
(ii) The circuit current is I
(iii) The voltage across the coil is VL
(iv) The resonant frequency fr
Arrange the above in increasing order of their numerical values.
Answer (Detailed Solution Below)
Equivalent Impedance Question 7 Detailed Solution
Download Solution PDFReq = 3 + 1.6 = 4.6 Ω
(i). The input impedance is Z
Z = 5.96
(ii) Circuit Current
(iii) Voltage across the coil is,
VL = 64.97 ∠ -61.36 °
(iv) Resonant frequency is given as,
Xl = 1.2 (f = 20 Hz)
2π fL = 1.2
Xc = 1 / (2πfC) = 5
fr = 40.82 Hz
Hence correct order is,
Z L
i
Calculate the value of Norton's current and Norton's equivalent resistance for the given circuit across the terminal AB.
Answer (Detailed Solution Below)
Equivalent Impedance Question 8 Detailed Solution
Download Solution PDFNorton's Theorem :
Any linear bilateral network consisting of multiple resistances and sources can be replaced by a resistor RN in parallel of Current source IN .
Calculation:
RN :
Disable all independent sources and find equivalent resistance.
RN = ( 20 || 10 ) + 20 = 26.6 ohm
IN :
Short circuited current
Let node voltage of 10 ohm is V
Apply nodal analysis
V = 2.5V
IN = V /20 = 125 mA
The equivalent circuit of a tunnel diode shown below has the total input impedance
i)
ii) Rs + ωRCj
iii)
iv)
Code:
Answer (Detailed Solution Below)
Equivalent Impedance Question 9 Detailed Solution
Download Solution PDFConcept:
The passive elements and their impedances are shown below table:
|
Element |
‘S’ domain |
Impedance in ‘ω’ |
|
Resistor |
R |
R |
|
Inductor (L) |
sL |
jωL |
|
Capacitor (C) |
|
|
Calculation:
The parallel equivalent impedance is:
Converting into the ‘ω’ form we get
The input impedance will be
Separating the real and imaginary parts
Equivalent Impedance Question 10:
Identify the type / status of circuit the below diagram represents.
Answer (Detailed Solution Below)
Equivalent Impedance Question 10 Detailed Solution
Concept:
Case I:
Series RLC load with inductive reactance more than the capacitive reactance implies it is equivalent to a series RL circuit.
Here, current lags voltage as shown
Case II:
Series RLC load with inductive reactance lesser than the capacitive reactance implies it is equivalent to a series RC circuit.
Here, current leads voltage as shown
Where,
VL = Inductor voltage
VC = Capacitor voltage
I = Current
V = Supply voltage
VR = Resistor Voltage
Application:
Given Circuit:
R = 6Ω, XL = j8, Xc = - j10
Zeq = (6 + j8) ∥ (- j10)
= 15 - j5 Ω
Net current from the supply is given by
Current is leading with respect to Voltage by 18.43∘
Therefore,
This indicates RC circuit
Equivalent Impedance Question 11:
In the following circuit, input impedance Zin(s) is ______
Answer (Detailed Solution Below)
Equivalent Impedance Question 11 Detailed Solution
Applying KCL at the node A in the Laplace domain, we get
Ix = 50 × 10-3 sVx(s) + 5 × 10-3s Vx(s) - 50 × 10-3s Vx(s)
Ix = sVx(s) [5 × 10-3]
Equivalent Impedance Question 12:
A 120 V, 20 Hz source supplies a series circuit consisting of a 5 Ω capacitive reactance, a 1.6 Ω resistor, and a coil with resistance and inductive reactance of 3 Ω and 1.2 Ω respectively.
(i) The input impedance is Z
(ii) The circuit current is I
(iii) The voltage across the coil is VL
(iv) The resonant frequency fr
Arrange the above in increasing order of their numerical values.
Answer (Detailed Solution Below)
Equivalent Impedance Question 12 Detailed Solution
Req = 3 + 1.6 = 4.6 Ω
(i). The input impedance is Z
Z = 5.96
(ii) Circuit Current
(iii) Voltage across the coil is,
VL = 64.97 ∠ -61.36 °
(iv) Resonant frequency is given as,
Xl = 1.2 (f = 20 Hz)
2π fL = 1.2
Xc = 1 / (2πfC) = 5
fr = 40.82 Hz
Hence correct order is,
Z L
i
Equivalent Impedance Question 13:
Calculate the value of Norton's current and Norton's equivalent resistance for the given circuit across the terminal AB.
Answer (Detailed Solution Below)
Equivalent Impedance Question 13 Detailed Solution
Norton's Theorem :
Any linear bilateral network consisting of multiple resistances and sources can be replaced by a resistor RN in parallel of Current source IN .
Calculation:
RN :
Disable all independent sources and find equivalent resistance.
RN = ( 20 || 10 ) + 20 = 26.6 ohm
IN :
Short circuited current
Let node voltage of 10 ohm is V
Apply nodal analysis
V = 2.5V
IN = V /20 = 125 mA
Equivalent Impedance Question 14:
In an LCR series circuit, source of emf is:
E = 30 sin (100t) and R = 120 Ω, L = 100 mH, C = 100 µF
(A) The numerical value of impedance
(B) The numerical value of Resistance R
(C) The numerical value of capacitive reactance
(D) The numerical value of inductive reactance
Arrange the values of quantities mentioned in (A, B, C, D) in increasing order.
Answer (Detailed Solution Below)
Equivalent Impedance Question 14 Detailed Solution
The correct answer is - (D), (C), (B), (A)
Key Points
- Impedance (Z)
- For an LCR series circuit, the impedance Z is given by the formula: Z = √(R² + (XL - XC)²).
- Here, R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.
- Resistance (R)
- The resistance R is given directly as 120 Ω.
- Inductive Reactance (XL)
- The inductive reactance XL is given by the formula: XL = ωL, where ω is the angular frequency (100 rad/s) and L is the inductance.
- Using the values: XL = 100 × 100 × 10-3 = 10 Ω.
- Capacitive Reactance (XC)
- The capacitive reactance XC is given by the formula: XC = 1 / (ωC), where ω is the angular frequency (100 rad/s) and C is the capacitance.
- Using the values: XC = 1 / (100 × 100 × 10-6) = 100 Ω.
Additional Information
- Impedance Calculation
- Using the values calculated above, we have: Z = √(120² + (10 - 100)²) = √(120² + (-90)²) = √(14400 + 8100) = √22500 = 150 Ω.
- Order of Values
- From the values calculated, we get the following numerical order:
- XL = 10 Ω
- R = 120 Ω
- XC = 100 Ω
- Z = 150 Ω
- From the values calculated, we get the following numerical order:
Equivalent Impedance Question 15:
The equivalent circuit of a tunnel diode shown below has the total input impedance
i)
ii) Rs + ωRCj
iii)
iv)
Code:
Answer (Detailed Solution Below)
Equivalent Impedance Question 15 Detailed Solution
Concept:
The passive elements and their impedances are shown below table:
|
Element |
‘S’ domain |
Impedance in ‘ω’ |
|
Resistor |
R |
R |
|
Inductor (L) |
sL |
jωL |
|
Capacitor (C) |
|
|
Calculation:
The parallel equivalent impedance is:
Converting into the ‘ω’ form we get
The input impedance will be
Separating the real and imaginary parts