Kirchhoff’s Rules MCQ Quiz - Objective Question with Answer for Kirchhoff’s Rules - Download Free PDF

Key Points

• The potential at point A is given as 20 V, and there is no potential drop across the circuit element between A and B.
• Point B is connected directly to point A, without any resistive or reactive element causing a voltage change.
• The circuit diagram shows no components like resistors, capacitors, or batteries between points A and B.
• Thus, the potential at point B is the same as at point A, which is 20 V.

The correct answer is: Option 2) Energy

Explanation:

Kirchhoff’s Second Law states that the algebraic sum of the potential differences (voltages) in any closed loop or mesh of an electrical circuit is always zero.

Mathematically: ∑V = 0 around any closed loop

This law is a direct consequence of the law of conservation of energy.

It implies that the energy gained by charges in a circuit (e.g., via batteries) is exactly equal to the energy lost (e.g., across resistors, capacitors, etc.).

We are given the circuit with two batteries and resistors connected as shown in the diagram. To find the current in the 1Ω resistor, we will apply Kirchhoff's Current Law (KCL) at point Q after connecting Q to the ground.

By applying KCL at point Q, we know that the incoming current at Q equals the outgoing current from Q:

Incoming current at Q = outgoing current from Q

V + 6 / 3 = V - V / 5

Solving this equation:

[V + (6 / 3)] = [V - (V / 5)]

[1 + 1/3 + 1/5]V = 9 - 10

V = -0.13 V

The current in the 1Ω resistance is found by using Ohm's Law:

I = V / R = -0.13 / 1 = 0.13 A from Q to P.

Therefore, the current in the 1Ω resistor is 0.13 A from Q to P (Option 3).

If a resistance is \(R\) is put in parallel across \(18 \Omega\), the effective resistance in arm AD will be \(\dfrac{18R}{18+R}\)

\(\dfrac { 4 }{ 6 } =\dfrac { 8 }{ 18\times R/(18+R) } \Rightarrow R=36\Omega \)

Calculation:

From Kirchhoff's first law at junction P, we have:

I₁ + I₂ = 6 A

From Kirchhoff's second law to the closed circuit PQR:

-2I₁ - 2I₁ + 2I₂ = 0

=> -4I₁ + 2I₂ = 0

2I₁ - I₂ = 0

Adding both equations, we get:

3I₁ = 6

=> I₁ = 2 A

I₂ = 6 - 2 = 4 A

Thus, the currents are I₁ = 2 A and I₂ = 4 A.

CONCEPT:

There are two types of Kirchoff’s Laws:

• Kirchoff’s first law: This law is also known as junction rule or current law (KCL). According to it the algebraic sum of currents meeting at a junction is zero i.e. Σ i = 0.

​

• In a circuit, at any junction, the sum of the currents entering the junction must be equal the sum of the currents leaving the junction i.e., i1 + i3 = i2 + i4
  • This law is simply a statement of “conservation of charge” as if current reaching a junction is not equal to the current leaving the junction, the charge will not be conserved.
• Kirchoff’s second law: This law is also known as loop rule or voltage law (KVL) and according to it “the algebraic sum of the changes in potential in a complete traversal of a mesh (closed-loop) is zero”, i.e. Σ V = 0.
  • This law represents “conservation of energy” as if the sum of potential changes around a closed loop is not zero, unlimited energy could be gained by repeatedly carrying a charge around a loop.

EXPLANATION:

1. Kirchhoff’s Current Law (KCL) is based on the conservation of charge. So option 1 is correct.
2. Kirchhoff’s Voltage Law (KVL) is based on the conservation of energy.
3. Ohm's law gives the relation between electric current and potential difference.
4. Coulomb's law gives the force between two charges separated by some distance.

CONCEPT:

• The difference of electric potential between two points is called potential difference.
• According to Ohm’s law: The potential difference across a resistor in a circuit is directly proportional to the current flowing in it.

V = R I

Where V is potential difference, R is resistance and I is current.

• Kirchhoff’s Voltage Law (KVL): It states that “in any closed loop network, the algebraic sum of all voltages within the loop must be equal to zero.

CALCULATION:

Let I be the electric current flowing in the circuit.

Here we will apply the KVL (start from the point A), we get

2 × (- I) + 6 – 8 I – 4 = 0

10 I = 2

Current (I) = 2/10 = 1/5 A = 0.2 A

Concept:

There are two types of Kirchoff’s Laws:

Kirchoff’s first law:

• This law is also known as junction rule or current law (KCL). According to it the algebraic sum of currents meeting at a junction is zero i.e. Σ i = 0.

​

• In a circuit, at any junction, the sum of the currents entering the junction must be equal the sum of the currents leaving the junction i.e., i1 + i3 = i2 + i4
• This law is simply a statement of “conservation of charge” as if current reaching a junction is not equal to the current leaving the junction, charge will not be conserved.

Kirchoff’s second law:

• This law is also known as loop rule or voltage law (KVL) and according to it “the algebraic sum of the changes in potential in the complete traversal of a mesh (closed-loop) is zero”, i.e. Σ V = 0.
• This law represents “conservation of energy” as if the sum of potential changes around a closed loop is not zero, unlimited energy could be gained by repeatedly carrying a charge around a loop.
• If there are n meshes in a circuit, the number of independent equations in accordance with loop rule will be (n - 1).

Here, the assumed current I causes a + ve drop of voltage when flowing from +ve to – ve potential while – ve drop of voltage when a current flowing from – ve to + ve for the above circuit,

 If we apply KVL,

−V + I R₁ + I R₂ = 0

So, algebraic sum of the voltage around a closed loop in a circuit must be zero.

Explanation:

The Kirchoff’s Voltage law states that the algebraic sum of the voltage around a closed loop in a circuit must be zero.

CONCEPT:

There are two types of Kirchoff’s Laws:

• Kirchoff’s first law: This law is also known as junction rule or current law (KCL). According to it the algebraic sum of currents meeting at a junction is zero i.e. Σ i = 0.
• Kirchoff’s second law: This law is also known as loop rule or voltage law (KVL) and according to it “the algebraic sum of the changes in potential in complete traversal of a mesh (closed loop) is zero”, i.e. Σ V = 0.
  • This law represents “conservation of energy” as if the sum of potential changes around a closed loop is not zero, unlimited energy could be gained by repeatedly carrying a charge around a loop.

EXPLANATION:

• The algebraic sum of changes in potential around any closed loop must be zero." This statement represents Kirchhoff’s Loop Rule. So option 2 is correct.

EXTRA POINTS:

• Ampere's Circuital Law: It gives the relationship between the current and the magnetic field created by it.
  • This law says that, the integral of magnetic field density (B) along an imaginary closed path is equal to the product of current enclosed by the path and permeability of the medium.

\(\oint \vec B.\overrightarrow {dl} = {\mu _0}I\)

• Force acting on a charged particle is given by Lorentz hence it is known as Lorentz force and it is expresses \(\overrightarrow {F} = \;q\left[ {\vec E - \vec v \times \vec B} \right]\;\)

Net Force acting on charge = F

Force acting on the charge due to electric field = qE

• Biot-Savart Law: The law who gives the magnetic field generated by a constant electric current is Biot-savart law.

Let us take a current carrying wire of current I and we need to find the magnetic field at a distance r from the wire then it is given by:

\(d\vec B = \;\frac{{{\mu _0}\;I}}{{4\pi }}\left( {\frac{{\overrightarrow {dl} \times \vec r}}{{{r^3}}}} \right)\)

Where, μ0 = the permeability of free space/vacuum (4π × 10-7 T.m/A), dl = small element of wire and \(\hat{r}\)= the unit position vector of the point where we need to find the magnetic field.

CONCEPT:

• According to Ohm’s law: The potential difference across a resistor in a circuit is directly proportional to the current flowing in it.

V = R I

Where V is potential difference, R is resistance and I is current.

• Kirchhoff’s current law (KCL): It states that, the total current entering a circuit’s junction is exactly equal to the total current leaving the same junction.

EXPLANATION:

Let potential at O is V’ and all the current is originating from the point O.

According to the KCL, the sum of all the current originating from the point O will be equal to zero.

Use Ohm’s law to final total current originating from O:

Current in OA + Current in OB + Current in OC = 0

(V – 8)/2 + (V – 4)/4 + (V – 2)/2 = 0

(2 V – 16 + V – 4 + 2 V – 4)/ 4= 0

5 V – 24 = 0

Concept:

There are two types of Kirchoff’s Laws:

Kirchoff’s first law:

• This law is also known as junction rule or current law (KCL). According to it the algebraic sum of currents meeting at a junction is zero i.e. Σ i = 0.

​

• In a circuit, at any junction, the sum of the currents entering the junction must be equal to the sum of the currents leaving the junction i.e., i1 + i3 = i2 + i4
• This law is simply a statement of “conservation of charge” as if the current reaching a junction is not equal to the current leaving the junction, the charge will not be conserved.

Kirchoff’s second law:

• This law is also known as loop rule or voltage law (KVL) and according to it “the algebraic sum of the changes in potential in the complete traversal of a mesh (closed-loop) is zero”, i.e. Σ V = 0.
• This law represents “conservation of energy” as if the sum of potential changes around a closed loop is not zero, unlimited energy could be gained by repeatedly carrying a charge around a loop.
• If there are n meshes in a circuit, the number of independent equations in accordance with the loop rule will be (n - 1).

Explanation:

• Therefore from above, it is clear that Kirchhoff's first law i.e. ∑i = 0 at a junction is based on the law of conservation of charge.

Hence, option Conservation of current and charge is correct.

There are two types of Kirchoff’s Laws:

Kirchoff’s first law:

• This law is also known as junction rule or current law (KCL). According to it the algebraic sum of currents meeting at a junction is zero i.e. Σ i = 0.

​

• In a circuit, at any junction, the sum of the currents entering the junction must be equal to the sum of the currents leaving the junction i.e., i1 + i3 = i2 + i4
• This law is simply a statement of “conservation of charge” as if the current reaching a junction is not equal to the current leaving the junction, the charge will not be conserved.

Kirchoff’s second law:

• This law is also known as loop rule or voltage law (KVL) and according to it “the algebraic sum of the changes in potential in a complete traversal of a mesh (closed-loop) is zero”, i.e. Σ V = 0.
• This law represents “conservation of energy” as if the sum of potential changes around a closed loop is not zero, unlimited energy could be gained by repeatedly carrying a charge around a loop.
• If there are n meshes in a circuit, the number of independent equations in accordance with the loop rule will be (n - 1).

EXPLANATION:

• From the above, it is clear that Kirchhoff's laws for electrical circuits are based on the conservation of charge and energy. Therefore option 2 is correct.

CONCEPT:

There are two types of Kirchhoff’s Laws:

Kirchhoff’s first law: This law is also known as junction rule or current law (KCL). According to it the algebraic sum of currents meeting at a junction is zero i.e. Σ i = 0.

​

• In a circuit, at any junction the sum of the currents entering the junction must be equal the sum of the currents leaving the junction i.e., i₁ + i₃ = i₂ + i₄
• This law is simply a statement of “conservation of charge” as if current reaching a junction is not equal to the current leaving the junction, charge will not be conserved.

Kirchhoff’s second law: This law is also known as loop rule or voltage law (KVL) and according to it “the algebraic sum of the changes in potential in complete traversal of a mesh (closed loop) is zero”, i.e. Σ V = 0.

• This law represents “conservation of energy” as if the sum of potential changes around a closed loop is not zero, unlimited energy could be gained by repeatedly carrying a charge around a loop.

EXPLANATION:

According to junction rule or current law:

Total current entering = Total current leaving the circuit

Here, Total current leaving = 4 A + 2 A + 1 A = 7 A

So total current entering = Total current leaving = 7 A

• This current will enter from DO and hence current in DO will flow from D to O and it is equal to 7 A. So option 3 is correct.

CONCEPT:

There are two types of Kirchoff’s Laws:

Kirchoff’s first law:

• This law is also known as junction rule or current law (KCL). According to it the algebraic sum of currents meeting at a junction is zero i.e. Σ i = 0.
• In a circuit, at any junction the sum of the currents entering the junction must be equal the sum of the currents leaving the junction.
• This law is simply a statement of “conservation of charge” as if current reaching a junction is not equal to the current leaving the junction, charge will not be conserved.

Kirchoff’s second law:

• This law is also known as loop rule or voltage law (KVL) and according to it “the algebraic sum of the changes in potential in complete traversal of a mesh (closed loop) is zero”, i.e. Σ V = 0.
• This law represents “conservation of energy” as if the sum of potential changes around a closed loop is not zero, unlimited energy could be gained by repeatedly carrying a charge around a loop.
• If there are n meshes in a circuit, the number of independent equations in accordance with loop rule will be (n - 1).

EXPLANATION:

• From above it clear that "The sum of emf’s and potential differences around a closed loop equals zero" is a consequence of conservation of energy

CONCEPT:

There are two types of Kirchoff’s Laws:

Kirchoff’s first law:

• This law is also known as junction rule or current law (KCL). According to it the algebraic sum of currents meeting at a junction is zero i.e. Σ i = 0.

• In a circuit, at any junction, the sum of the currents entering the junction must be equal the sum of the currents leaving the junction i.e., i1 + i3 = i2 + i4
• This law is simply a statement of “conservation of charge” as if current reaching a junction is not equal to the current leaving the junction, the charge will not be conserved.

Kirchoff’s second law:

• This law is also known as loop rule or voltage law (KVL) and according to it “the algebraic sum of the changes in potential in a complete traversal of a mesh (closed-loop) is zero”, i.e. Σ V = 0.
• This law represents “conservation of energy” as if the sum of potential changes around a closed loop is not zero, unlimited energy could be gained by repeatedly carrying a charge around a loop.
• If there are n meshes in a circuit, the number of independent equations in accordance with the loop rule will be (n - 1).

EXPLANATION:

• From above it is clear that Kirchoff’s second law is also known as loop rule or voltage law (KVL). Therefore statement 1 is correct.
• From above it is clear that Kirchoff’s second law represents “conservation of energy” as if the sum of potential changes around a closed loop is not zero, unlimited energy could be gained by repeatedly carrying a charge around a loop. Therefore statement 2 is correct.