300+ Network Theorem MCQ – Objective Question Answer for Network Theorem Quiz

We know if there are n loops in the circuit, n mesh equations can be formed. So as there are 2 loops in the circuit. So 2 mesh equations can be formed.

Through the resistor R2 both the currents, I1 and I2 are flowing. So the current through R2 will be I1 − I2.

Number of mesh equations

= B − (N − 1).

Given a number of branches = 5 and number of nodes = 4.

So Number of mesh equations = 5 − (4 − 1) = 2.

Consider current I1 (CW) in loop 1 and I2 (ACW) in loop 2.

So, the equations will be

Vx + I2 − I1 = 0.

I1 = 5/2 = 2.5A

I2 = 4Vx/4

= Vx. Vx + Vx − 2.5 = 0.

Vx  = 1.25V.

According to mesh analysis,

(1 + 3 + 6)I1 – 3(I2) – 6(I3) = 10

− 3(I1) + (2 + 5 + 3)I2

= 4 − 6(I1) + 10(I3) = − 4 + 20

On solving the above equations, I1 = 4.3A.

According to mesh analysis

(1 + 3 + 6)I1 – 3(I2) – 6(I3) = 10.

− 3(I1) + (2 + 5 + 3)I2  = 4.

− 6(I11) + 10(I3) = − 4 + 20

On solving the above equations,

I2  = 1.7A.

According to mesh analysis

(1 + 3 + 6)I1 – 3(I2) – 6(I3) = 10

− 3(I1) + (2 + 5 + 3)I2  = 4.

− 6(I1) + 10(I3) = − 4 + 20.

On solving the above equations, I3  = 4.7A.

Applying mesh analysis

5(I1) + 2(I1 − I2) = 10

10(I2) + 2(I2 − I1) + 40 = 0.

On solving

I1  = 0.5A, I2  = − 3.25A.

So current through R2 resistor is 0.5 − ( − 3.25) = 3.75 A

The node equation is:

− 2 + 8 + V/10 = 0 = > 6 + v/10 = 0 = > v = − 10 × 6 = − 60V

Solving this equation, we get V = − 60V.

The nodal equations are:

2V1 − V2 = − 4
− 4V1 + 5V2 = 88

Solving these equations simultaneously, we get

V1 = 11.33V and V2 = 26.67V.

The nodal equation is:

(V − 10)/2 + (V − 7)/3 + V/1 = 0

Solving for V, we get V = 4V.

The nodal equations, considering V1, V2 and V3 as the first, second and third node respectively, are:

− 8 + (V1 − V2)/3 − 3 + (V1 − V3)/4 = 0
3 + V2 + (V2 − V3)/7 + (v2 − V1)/3 = 0
− 2.5 + (V3 − V2)/7 + (V3 − V1)/4 + V3/5 = 0

Solving the equations simultaneously, we get

V1 = 30.77V, V2 = 7.52V and V3 = 18.82V.

The nodal equations are:

0.3V1 − 0.2V2 = 16

− V1 + 3V2 = − 15

Solving these equations simultaneously, we get

V1 = 64.28V and V2 = 16.42V.

The nodal analysis uses Kirchhoff’s Current Law to find all the node voltages. Hence it is a method used to determine the voltage.

One node is taken as a reference node so, the number of equations we get is always one less than the number of nodes in the circuit, hence for 10 nodes we get 9 equations.

Nodal analysis can be applied for both planar and non-planar networks since each node, whether it is planar or non-planar, can be assigned a voltage.

In the nodal analysis, one node is treated as the reference node and the voltage at that point is taken as 0.

Number of equations = N − 1 = 7.

So as there are 8 nodes in the network, we can get 7 number of equations in the nodal analysis.

Nodal analysis is applicable for both planar and non-planar networks. Each node in a circuit can be assigned a number or a letter.

In nodal analysis, only one node is taken as a reference node. And the node voltage is the voltage of a given node with respect to one particular node called the reference node.