Network Elements and the Concept of Circuit Easy Questions and Answers | Page - 56

Network Elements and the Concept of Circuit

Consider the following properties of a particular network theorem:
1. The theorem is not concerned with type of elements.
2. The theorem is only based on the two Kirchoff’s laws.
3. The reference directions of the branch voltages and currents are arbitarary except that they have to satisfy Kirchoff’s laws.
Which one of the following theorems has the above characteristics?

1. Thevenin’s theorem
1. Norton’s theorem
1. Tellegen’s theorem
1. Superposition theorem

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Tallegen’s theorem
• Is not concerned with type of elements
• Is only based on the Kirchoff’s laws.
• In Tallegen’s theorem the reference directions of the branch voltages and currents are arbitarary except that have to satisfy Kirchoff’s laws.

Correct Option: C

Tallegen’s theorem
• Is not concerned with type of elements
• Is only based on the Kirchoff’s laws.
• In Tallegen’s theorem the reference directions of the branch voltages and currents are arbitarary except that have to satisfy Kirchoff’s laws.

Consider the following circuit:

For the above circuit, which one of the following statements is correct? The voltage V0 is independent of R, if the input signal frequency —

1. is 1
  LC
1. is 1
  [2 LC]
1. is LC
1. has any value

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V₀ should be independent from R when no current in R. It will be possible when R → ∞ or there should be series resonance in LC circuit with adding resistance Condition of series resonance,
Z = R₁ + j ωL - 1 = J ωL - 1 = 0
ωC ωC

ω² = 1
LC

or ω = 1
√LC

Correct Option: A

V₀ should be independent from R when no current in R. It will be possible when R → ∞ or there should be series resonance in LC circuit with adding resistance Condition of series resonance,
Z = R₁ + j ωL - 1 = J ωL - 1 = 0
ωC ωC

ω² = 1
LC

or ω = 1
√LC

Which one of the following statements is not correct?

1. A tree contains all the vertices of its graph
1. A circuit contains all the vertices of its graph
1. The number of f-circuits is the same as the number of chords
1. There are at least two edges in a circuit

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NA

Correct Option: B

NA

An RLC series circuit has a resistance R of 20 Ω and a current which lags behind the applied voltage by 45º. If the voltage across the inductor is twice the voltage across the capacitor, what is the value of inductive reactance?

1. 10 Ω
1. 20 Ω
1. 40 Ω
1. 60 Ω

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Given R = 20Ω Current lags behind the applied voltage by 45º
and V_L = 2 V_C
IX_L = 2IX_C
or X_L = 2X_C.......(i)
tan 45° = V_L − V_C = I(X_L − X_C) = X_L − X_C
V_R I_R R

1 = X_L − X_C
R

or X_L – X_C = R = 20 ....(ii)
From equations (i) and (ii)
X_L − X_L = 20
2

or X_L = 40 Ω
This is the required value of inductive reactance.

Correct Option: C

Given R = 20Ω Current lags behind the applied voltage by 45º
and V_L = 2 V_C
IX_L = 2IX_C
or X_L = 2X_C.......(i)
tan 45° = V_L − V_C = I(X_L − X_C) = X_L − X_C
V_R I_R R

1 = X_L − X_C
R

or X_L – X_C = R = 20 ....(ii)
From equations (i) and (ii)
X_L − X_L = 20
2

or X_L = 40 Ω
This is the required value of inductive reactance.

R and C are connected in parallel across a sinusoidal voltage source of 240 V. If the currents through the source and the capacitor are 5A and 4A, respectively; what is the value of R?

1. 24Ω
1. 48Ω
1. 80Ω
1. 240Ω

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Given R and C are connected in parallel across a sinusoidal voltage source of 240V.

I_R = √I_s² − I_C²
I_R = √(5)² − (4)² = 3A
R = V = 240 = 80 Ω
I_R 3

Correct Option: C

Given R and C are connected in parallel across a sinusoidal voltage source of 240V.

I_R = √I_s² − I_C²
I_R = √(5)² − (4)² = 3A
R = V = 240 = 80 Ω
I_R 3