Network Elements MCQ Quiz - Objective Question with Answer for Network Elements - Download Free PDF

Concept:

Each electrical quantity has a standard dimensional formula derived using base physical quantities: Mass (M), Length (L), Time (T), and Current (I or A).

Step-by-step Matching:

1. Resistance (A):

From Ohm's law:

Voltage (V) has dimensions of Current (I) is I

So, → This matches with option F

2. Inductance (B):

From the formula:

So, using the Voltage dimension again: → This matches option E

3. Capacitance (C):

From:

Charge (Q) has dimension and the voltage is

So, → This matches with option D

Final Matching:

• A (Resistance) → F
• B (Inductance) → E
• C (Capacitance) → D

Answer:

Option 3) {(A, F), (B, E), (C, D)}

Concept:

When capacitors are connected in series, the total (effective) capacitance is given by:

The maximum voltage across the combination is limited by the capacitor which reaches its voltage rating first, considering how voltage divides in series based on inverse of capacitance.

Given:

• C₁ = 0.005 µF = 5 nF, V_max1 = 40 V
• C₂ = 0.02 µF = 20 nF, V_max2 = 100 V

Step 1: Effective Capacitance

Step 2: Maximum DC Voltage

In series, same charge appears across both capacitors. Let charge Q be the same:

Let V₂ = x, then V₁ = 4x ⇒ Total voltage V_total = V₁ + V₂ = 4x + x = 5x

Now, apply voltage limit for C₁: V₁ ≤ 40 V ⇒ 4x ≤ 40 ⇒ x ≤ 10 V

⇒ Total V_total = 5x = 50 V (Maximum allowable without exceeding capacitor voltage ratings)

Hence,  the correct answer is option 2

We have redrawn the circuit by taking the potential as Vs across the current source & V_A across the 12 Ω resistance.

Applying KCL at node A

The net current flowing into the A terminal will equal the net current flowing out of the terminal.

2 = 1 + 

⇒V_A = 12 V

We know that the current flowing across the 1Ω resistance is 2 A.

⇒ Vs =  14 V

Thus the voltage across the current source is 14 V

Concept:

When voltage varies linearly with time, the average voltage is used to calculate total energy.

Energy delivered = Current × Average Voltage × Time

Given:

• Initial voltage V_start = 10 V
• Final voltage V_end = 9 V
• Current I = 1 A (constant)
• Time t = 1 hour = 3600 seconds

Step-by-step Calculation:

Average voltage =

Energy = I × V_avg × t = 1 × 9.5 × 3600 = 34200 J = 34.2 kJ

Concept:

The voltage across a capacitor is given by:

Where is capacitance, and is the current through the capacitor.

Given:

Capacitance,

Current waveform is a triangle from 0 to 10 mA over 4 ms

We are to find voltage at

Calculation:

From 0 to 4 ms, current increases linearly ⇒ it's a triangle

Area under the triangle (charge):

From 4 ms to 5 ms, current = 0 ⇒ no additional charge

Voltage:

Answer:

Option 3) 200 mV

Ohm’s law: Ohm’s law states that at a constant temperature, the current through a conductor between two points is directly proportional to the voltage across the two points.

Voltage = Current × Resistance

V = I × R

V = voltage, I = current and R = resistance

The SI unit of resistance is ohms and is denoted by Ω.

It helps to calculate the power, efficiency, current, voltage, and resistance of an element of an electrical circuit.

Limitations of ohms law:

• Ohm’s law is not applicable to unilateral networks. Unilateral networks allow the current to flow in one direction. Such types of networks consist of elements like a diode, transistor, etc.
• Ohm’s law is also not applicable to non – linear elements. Non-linear elements are those which do not have current exactly proportional to the applied voltage that means the resistance value of those elements’ changes for different values of voltage and current. An example of a non-linear element is thyristor.
• Ohm’s law is also not applicable to vacuum tubes.

Concept:

Ideal voltage source: An ideal voltage source have zero internal resistance.

Practical voltage source: A practical voltage source consists of an ideal voltage source (VS) in series with internal resistance (RS) as follows.

An ideal voltage source and a practical voltage source can be represented as shown in the figure.

Ideal current source: An ideal current source has infinite resistance. Infinite resistance is equivalent to zero conductance. So, an ideal current source has zero conductance.

Practical current source: A practical current source is equivalent to an ideal current source in parallel with high resistance or low conductance.

Ideal and practical current sources are represented as shown in the below figure.

• When an ideal voltage source and an ideal current source in series, the combination has an ideal current sources property.
• Current in the circuit is independent of any element connected in series to it.

Explanation:

In a series circuit, the current flows through all the elements is the same. Thus, any element connected in series with an ideal current source is redundant and it is equivalent to an ideal current source only.

In a parallel circuit, the voltage across all the elements is the same. Thus, any element connected in parallel with an ideal voltage source is redundant and it is equivalent to an ideal voltage source only.

Concept:

When resistances are connected in parallel, the equivalent resistance is given by

When resistances are connected in series, the equivalent resistance is given by

Calculation:

Given that R₁ = R₂ = R₃ = 6 Ω and all are connected in parallel.

⇒ R_eq = 2 Ω

When capacitors are connected in series across DC voltage:

• The charge of each capacitor is the same and the same current flows through each capacitor in the given time.
• The voltage across each capacitor is dependent on the capacitor value.

When capacitors are connected in parallel across DC voltage:

• The charge of each capacitor is different and the current flows through each capacitor in the given time are also different and depend on the value of the capacitor.
• The voltage across each capacitor is the same.

The circuit after removing the voltage source

The total resistance of the new circuit will be the equivalent resistance of the network.

R_eq = R_t = 3 + 2 + 2 = 7 Ω 

The equivalent resistance of the network is 7 Ω.

 Mistake PointsWhile finding the equivalent resistance of the network, don't consider the internal resistance of the voltage source. Please read the question carefully it is mentioned in the question as well.

There are two kinds of voltage or current sources:

Independent Source: It is an active element that provides a specified voltage or current that is completely independent of other circuit variables.

Dependent Source: It is an active element in which the source quantity is controlled by another voltage or current in the circuit.

Concept-

The dimensional formula is defined as the expression of the physical quantity in terms of mass, length, time and ampere.

Explanation-

Power – It is defined as rate of doing work.

Where, P = power, W = work done and t = time.

Now,

Dimensional formula of work (W) = [ML²T^-2]

Dimensional formula of time (t) = [T¹]

∴ The dimensional formula of power P is [ML²T^-3].

Concept:

The resistance of conductor changes when the temperature of that conductor changes.

New resistance is given by:

Where R_t = the resistance of the conductor after temperature changes

R₀ = the resistance of the conductor before temperature changes

α = temperature coefficient

ΔT = final temperature – initial temperature

Calculation:

R₀ = ?

α = 0.00125/°C

T₁ = 300 k = 300 - 273 = 27°C

T₂ = 1100 k = 1100 – 273 = 827°C

Resistance at T₁ =27°C

R_27°C =  R0  {1+ (0.00125 × 27)}

R0  = 1 / {1+ (0.00125 × 27)}  

R₀ = 0.967

Now at T₂  =  827 *C

R = 0.967 * {(1+ 0.00125 × 827)

R = 1.967 ohms 

Here the nearest option is 2ohm.

Concept:

Electric current: If the electric charge flows through a conductor, we say that there is an electric current in the conductor.

If Q charge flow through the conductor for ‘t’ seconds, then the current given by that conductor is

Q = I × t

I = current

t = times

Calculation:

Given I = 5 amp

t = 3 min = 180 sec

Q = I × t