This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Mesh Analysis”.

1. If there are M branch currents, then we can write ___________ number of independent equations.

a) M-2

b) M-1

c) M

d) M+1

View Answer

Explanation: If there are M branch currents, then we can write M number of independent equations. Number of independent equations = M.

2. If there are M meshes, B branches and N nodes including reference node, the number of mesh currents is given as M=?

a) B + (N+1)

b) B + (N-1)

c) B-(N+1)

d) B-(N-1)

View Answer

Explanation: If there are M meshes, B branches and N nodes including reference node, the number of mesh currents is given as M= B-(N-1).

3. Determine the current I_{1} in the circuit shown below using mesh analysis.

a) 0.955∠-69.5⁰

b) 0.855∠-69.5⁰

c) 0.755∠-69.5⁰

d) 0.655∠-69.5⁰

View Answer

Explanation: The equation for loop 1 is I

_{1}(j4) + 6(I

_{1}-I

_{2}) = 5∠0⁰. The equation for loop 2 is 6(I

_{1}-I

_{2}) + (j3) I

_{2}+ (2) I

_{2}= 0. Solving the above equations, I

_{1}= 0.855∠-69.5⁰.

4. In the circuit shown in question 3 find the current I_{2}.

a) 0.5∠-90⁰

b) 0.6∠-90⁰

c) 0.7∠-90⁰

d) 0.8∠-90⁰

View Answer

Explanation: The equation for loop 1 is I

_{1}(j4) + 6(I

_{1}-I

_{2}) = 5∠0⁰. The equation for loop 2 is 6(I

_{1}-I

_{2}) + (j3) I

_{2}+ (2) I

_{2}= 0. Solving the above equations, I

_{2}= 0.6∠-90⁰.

5. Find Z_{11}, Z_{12}, Z_{13} obtained from the mesh equations in the circuit shown below.

a) (8+j4) Ω, 5 Ω, 0Ω

b) (8-j4) Ω, 5 Ω, 0Ω

c) (8+j4) Ω, – 5 Ω, 0Ω

d) (8-j4) Ω, -5 Ω, 0Ω

View Answer

Explanation: Z

_{11}= self impedance of loop 1 = (5 + 3 – j4) Ω. Z

_{12}= Impedance common to both loop 1 and loop2 = -5Ω. Z

_{13}= No common impedance between loop1 and loop 3 = 0Ω.

6. Determine Z_{21}, Z_{22}, Z_{23} in the circuit shown in question 5.

a) 5Ω, (5-j1) Ω, j6 Ω

b) -5Ω, (5-j1) Ω, j6 Ω

c) -5Ω, (5+j1) Ω, j6 Ω

d) -5Ω, (5-j1) Ω, – j6 Ω

View Answer

Explanation: Z

_{21}= common impedance to loop 1 and loop 2 = -5 Ω. Z

_{22}= self impedance of loop2 = (5+j5-j6) Ω. Z

_{23}= common impedance between loop2 and loop 3 = – (-j6) Ω.

7. Find Z_{31}, Z_{32}, Z_{33} in the circuit shown in question 5.

a) 0Ω, j6Ω, (4-j6) Ω

b) 0Ω, -j6Ω, (4+j6) Ω

c) 0Ω, -j6Ω, (4-j6) Ω

d) 0Ω, j6Ω, (4+j6) Ω

View Answer

Explanation: Z

_{31}= common impedance to loop 3 and loop 1 = 0 Ω. Z

_{32}= common impedance between loop3 and loop 2 = – (-j6) Ω. Z

_{33}= self impedance of loop 3 = (4-j6) Ω.

8. Find the values of Z_{11}, Z_{22}, Z_{33} in the circuit shown below.

a) (4+j3) Ω, (3-j2) Ω, (5-j5) Ω

b) (4+j3) Ω, (3+j2) Ω, (5-j5) Ω

c) (4-j3) Ω, (3-j2) Ω, (5-j5) Ω

d) (4+j3) Ω, (3-j2) Ω, (5+j5 ) Ω

View Answer

Explanation: Z

_{11}= self impedance of loop 1 = (4 + j3) Ω. Z

_{22}= self impedance of loop2 = (j3+3+j4-j5) Ω. Z

_{33}= self impedance of loop 3 = (-j5+5) Ω.

9. Find the common impedances Z_{12}, Z_{13}, Z_{21}, Z_{23}, Z_{31}, Z_{32} respectively in the circuit shown in question 8.

a) -j3Ω, 0Ω, -j3Ω, j5Ω, 0Ω, j5Ω

b) j3Ω, 0Ω, -j3Ω, j5Ω, 0Ω, j5Ω

c) j3Ω, 0Ω, -j3Ω, j5Ω, 0Ω,- j5Ω

d) j3Ω, 0Ω, -j3Ω, -j5Ω, 0Ω, j5Ω

View Answer

Explanation: The common impedances Z

_{12}and Z

_{21}are Z

_{12}= Z

_{21}= -j3Ω. The common impedances Z

_{13}and Z

_{31}are Z

_{13}= Z

_{31}=0Ω. The common impedances Z

_{23}and Z

_{32}are Z

_{23}= Z

_{32}= j5Ω.

10. Find the value V_{2} in the circuit shown in question 9 if the current through (3+j4) Ω is zero.

a) 16∠-262⁰

b) 17∠-262⁰

c) 18∠-262⁰

d) 19∠-262⁰

View Answer

Explanation: The three loop equations are (4+j3)I

_{1}–(j3)I

_{2}= 20∠0⁰. (-j3)I

_{1}+ (3+j2)I

_{2}+ (j5)I

_{3}= 0. (j5)I

_{2}+ (5-j5)I

_{3}= -V

_{2}. The current through (3+j4) Ω is zero, I

_{2}= ∆

_{2}/∆ =0

4+j3 20∠0⁰ 0 ∆2 = | -j3 0 j5 | 0 -V2 5-j5

On solving, V_{2} = 17∠-262⁰.

**Sanfoundry Global Education & Learning Series – Network Theory.**

To practice all areas of Network Theory, __here is complete set of 1000+ Multiple Choice Questions and Answers__.