Thevenin's Theorem MCQ Quiz in বাংলা - Objective Question with Answer for Thevenin's Theorem - বিনামূল্যে ডাউনলোড করুন [PDF]

R_AB = 10 + 20 = 30 Ω

By KVL,

-15 – 100 + V_th = 0

⇒ V_th = 115 V

Concept:

To calculate Thevenin equivalent resistance RTH

Step 1: Open circuit the independent current source, short circuit the independent voltage source.

Step 2: Keep dependent sources as it is.

Step 3: Place a test voltage or current source from which terminal R_TH needs to be calculated.

Step 4: Calculate the V/I ratio from that terminal to determine RTH

Calculation:

Short circuit the independent voltage source.

Keep the dependent source as it is.

Place a test voltage source V_x.

Apply KVL on indicated loop:

⇒ -V_X + 3000I_X + 2000(V_X/4000 + I_X) = 0

⇒(-VX ) + 3000IX + VX/2 + 2000IX = 0

⇒(-VX/2) + 5000I_x = 0

⇒5000I_x=V_x/2

⇒  V_X/I_X = R_TH =  10 KΩ 

The correct answer is (option 1) i.e. 8 Ω 

Concept:

• Thevenin's equivalent voltage is the open circuit voltage across load terminal.
• Thevenin's equivalent resistance is the equivalent resistance across the load terminals after removing all voltage source.
• Independent Voltage source is replaced with short circuit and Independent current source is replaced with open circuit.

Calculation:

Now,voltage source is replaced with short circuit and current source is replaced with open circuit.

So, the circuit becomes

\(R_{th}=( 5\parallel20)+4\) Ω 

=4 + 4 = 8 Ω 

Concept:

According to Thevenin’s theorem, any linear circuit across a load can be replaced by an equivalent circuit consisting of a voltage source Vth in series with a resistor Rth as shown:

Vth = Open circuit Voltage at a – b (by removing the load), i.e.

If a linear circuit contains dependent sources only, i.e., there is no independent source present in the network, then the open-circuit voltage or Thevenin voltage will simply be zero. (Since there is no excitation present)

Calculation:

Given circuit can be drawn as,

Here, we have to calculate the voltage across the terminal ab which is  Thevenin voltage,

Since, voltage across 20 Ω = V_ab = V_TH

Let current I flowing through the circuit,

∴ V_TH = 20I = 20 × \(\frac{50}{5+20}\) = 40 V

Concept:

Thevenin's Theorem:

Any two terminal bilateral linear DC circuits can be replaced by an equivalent circuit consisting of a voltage source and a series resistor.

To solve Problems with Dependent Sources:

To find V_oc : Calculate the open-circuit voltage across load terminals. This open-circuit voltage is called Thevenin’s voltage (V_th).

To find R_th: 

To calculate Thevenin’s Resistance we should replace all independent current sources by Open circuit and Independent voltage sources by Short circuit (keep dependent sources as it is).

Circuits that have only dependent sources can’t function on their own so V_th and I_sc don’t exist but still they exhibit resistance, that resistance can be indirectly determined by V/I method by placing an active source across the terminals.

1. Place a voltage source of 1V across the terminal and find the current (I_T) flowing through it. Then,  

\({{\rm{R}}_{{\rm{th}}}} = {{\rm{R}}_{\rm{N}}} = \frac{{1{\rm{V}}}}{{{{\rm{I}}_{\rm{T}}}}}\)

(or) 

2. Place a current source of 1A across the terminals and find the voltage (V_t) across the current source. Then,

 \({{\rm{R}}_{{\rm{th}}}} = {{\rm{R}}_{\rm{N}}} = \frac{{{{\rm{V}}_{\rm{T}}}}}{{1{\rm{A}}}}\)

Application:

Applying KCL at a

\(\frac{{{V_{ab}}}}{5} + \frac{{{V_{ab}} - 10}}{5} = 1\)

\( {V_{ab}} = 7.5 = {V_{th}}\)

Now This circuit becomes a dead network can be energized by assuming a voltage source of V with Current flowing through it is I across a and b.

Now Apply Nodal Analysis we get,

\(\frac {V}{5}-I+\frac {V}{5}=0\ \)

\( R_{th}=\frac {V}{I}=2.5\Omega\)

Thevenin’s voltage is the open circuit voltage across the terminals a and b.

By using source transformation,

By using source transformation once again,

By applying KVL

30 + 15 I + 5I + 8 = 0

⇒ I = -1.9 A

By applying KVL

30 + 15I + V_ab = 0

⇒ V_ab = -15I – 30 = -15(-1.9) - 30

= -1.5 V

Concept:

The Thevenin resistance is the resistance looking back from load terminal with independent source replaced by its internal resistance(for ideal voltage source it will be zero hence short circuited and ideal current source it will be infinite hence open circuited).

Note: If there is/are dependent source/sources leave them as it is and calculate V/I ratio from the load terminal to determine thevenin's resistance.

Calculation:

Let 

Voltage at node n₁ is V_n1 , at n₂ is V_n2 and voltage across terminal AB is V.

Using KVL;

V_n1 = 200i_x + v_x

⇒Vn1 = vx + vx [∵ i_x =v_x/200]

Vn1 = 2v_x

Apply KCL at node n₁

(v_x/200 + 2v_x/200 + (2v_x - v)/200 = 0

⇒ v = 5v_x

Applying KCL at node n₂

1 + 0.01v_x = (v - 2v_x)/200

putting v = 5v_x, we get

v_x = 200 Volts,

Since v = 5v_x

v = 1000.

R_th = v/1

= 1000

Concept: 

In any linear, active, bilateral network consisting of energy sources, resistance etc with open terminals defined can be converted into a simple network consisting of voltage source in series with resistance.

Source transformation:

Explanation:

The given circuit is

Applying source transformation, we get the above circuit.

Now solve for 2 parallel resistance

i.e. 20 Ω and 5 Ω

∴ Req = \(\frac{20 \times 5}{25} = 4 \Omega \)

Again apply source transformation for 3/2 A source and R_eq the circuit obtained is

As circuit is open, current = 0. Assume potential at (A) to be +ve and apply KVL

-6 + 12 + V_AB = 0

⇒ V_AB = - 6 V

∴ option 2 is correct.

Concept:

Thevenin’s Theorem: 

A linear active resistive network which contains one or more independent or dependent voltage source or current sources can be replaced by a single voltage source (V_th) in series with equivalent resistance (R_th).

Where,

Vth is the open-circuit voltage. when, I = 0.

Rth is the Equivalent resistance seen from the load.

When,

1.  All independent sources are replaced by their internal impedances.
2.  All dependent voltage sources and current sources remain as they are.

Note: The theorem is not applicable to the network containing:

• Non-linear element.
• Unilateral element.

Norton’s Theorem: 

A linear, active resistive network that contains one or more independent or dependent voltage or current sources can be replaced by a single current source (I_SC) in shunt with equivalent resistance (Rth).

Where, 

I_SC is a short circuit current. when, V = 0.

R_th is the same as that of Thevenin's equivalent resistance.

We can say that Norton’s theorem is the converse of Thevenin’s theorem.

Concept:

The Thevenin voltage  V_TH used in Thevenin's Theorem is an ideal voltage source equal to the open circuit voltage at the terminals.

Calculation:

Remove the 20 Ω resistor and calculate the voltage between terminals A and B

V_A = 20 × 10/(10+10) = 10 V

V_B = 20 × 5/(20+5) = 4 V

V_AB = V_TH = (10 - 4) = 6 V