## Kirchhoff’s Laws and Network Solutions MCQ (Interview-Exam) Question-Answer

**Q.1** Find the value of I1, I2 and I3.

**A.** -1.29A, -0.566A, 1.91A

**B.** 1.91A, 0.566A, 1.29A

**C.** -0.566A, 1.29A, -1.91A

**D.** 1.29A, -0.566A, -1.91A

**Ans : **1.29A, -0.566A, -1.91A

**Explanation: ** Matrix(3,-2,0) (I1)=(5)

(-2,9,-4) (I2)=(0)

(0,-4,9) (I3)=(-15)

Solving this matrix equation, we get I1 = 1.29A, I2 = -0.566A and I3 = -1.91A.

**Q.2** Find the value of V, if the value of I3= 0A.

**A.** 6.5 V

**B.** 2.739V

**C.** 1.739 V

**D.** 4.5V

**Ans : **1.739 V

**Explanation: ** 5-3I1+2I2=0, 9I2-2I1=0, -4I2+V=0

On solving,V=1.739V.

**Q.3** Find the current in the 4 ohm resistor.

**A.** 0A

**B.** 20A

**C.** 5A

**D.** 2.2A

**Ans : **0A

**Q.4** Find the value of R if the power in the circuit is 1000W.

**A.** 9 ohm

**B.** 7 ohm

**C.** 10 ohm

**D.** 8 ohm

**Ans : **8 ohm

**Explanation: ** VI=P =>100I=1000 => I=10A.

Voltage across the 2 ohm resistor = 20V.

Voltage across the R resistor = 100-20= 80V.

R=V/I => R=80/10 = 8A.

**Q.5** Mesh analysis is generally used to determine_________.

**A.** Current

**B.** Power

**C.** Voltage

**D.** Resistance

**Ans : **Current

**Q.6** Nodal analysis is generally used to determine______.

**A.** Current

**B.** Power

**C.** Voltage

**D.** Resistance

**Ans : **Voltage

**Q.7** KCL is associated with_________

**A.** Nodal analysis

**B.** Neither mesh nor nodal

**C.** Mesh analysis

**D.** Both mesh and nodal

**Ans : **Nodal analysis

**Q.8** KVL is associated with___________.

**A.** Nodal analysis

**B.** Neither mesh nor nodal

**C.** Mesh analysis

**D.** Both mesh and nodal

**Ans : **Mesh analysis

**Explanation: ** I=V/R. Total resistance R = 20+40=60ohm. V=120V. I=120/60=2A.

**Q.9** Does the 15A source have any effect on the circuit?

**A.** No

**B.** Yes, only when the 10V source is removed

**C.** Yes

**D.** Cannot be determined

**Ans : **No

**Q.10** What is the current in the circuit?

**A.** 15A

**B.** 10A

**C.** 0A

**D.** 5A

**Ans : **0A

**Explanation: ** If we move in the clockwise direction, we get the total voltage to be equal to: -10-20+30 = 0V. Since I=V/R = 0/4=0, I=0A.

## Kirchhoff’s Laws:

**Kirchhoff’s Current Law (KCL):**States that the total current entering a junction in an electrical circuit is equal to the total current leaving the junction.

Mathematically expressed as ΣI_{in}= ΣI_{out}, where the sum of incoming currents equals the sum of outgoing currents at any node.**Kirchhoff’s Voltage Law (KVL):**Asserts that the total voltage around any closed loop in a circuit is equal to the sum of the individual voltage drops across the components.

Mathematically expressed as ΣV_{loop}= 0, where the sum of voltages in a closed loop is zero, indicating energy conservation.

## Network Solutions:

**Node Analysis:**A method of analyzing electrical circuits by applying KCL to each node.

Helps determine the voltages at different nodes in a circuit.**Mesh Analysis:**Involves applying KVL to each mesh (a loop that does not contain other loops) in a circuit.

Facilitates the calculation of mesh currents and subsequently the voltages across circuit elements.**Superposition Theorem:**States that the response in any element of a linear circuit is the algebraic sum of the individual responses caused by each independent source acting alone.

Enables the analysis of complex circuits with multiple sources by considering each source separately.**Thevenin’s Theorem:**Simplifies a complex circuit into an equivalent circuit consisting of a voltage source (Thevenin voltage) and a series resistor (Thevenin resistance).

Useful for analyzing the behavior of a circuit at a particular load without the need to consider the entire circuit.**Norton’s Theorem:**Similar to Thevenin’s Theorem but replaces the Thevenin voltage with a current source (Norton current) and the Thevenin resistance with a parallel resistor (Norton resistance).

Provides an alternative approach to simplifying and analyzing complex circuits.**Maximum Power Transfer Theorem:**States that the maximum power is transferred from a source to a load when the load resistance is equal to the source resistance.

Useful in optimizing power delivery in practical circuit design.