# Millman’s Theorem MCQ’s

This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Millman’s Theorem”.

1. According to Millman’s Theorem, if there are n voltage sources with n internal resistances respectively, are in parallel, then the value of equivalent voltage source is?

a) V^{‘}=(V_{1}G_{1}+V_{2}G_{2}+⋯.+V_{n}G_{n})

b) V^{‘}=((V_{1}G_{1}+V_{2}G_{2}+⋯.+V_{n}G_{n}))/((1/G_{1}+1/G_{2}+⋯1/G_{n}))

c) V^{‘}=((V_{1}G_{1}+V_{2}G_{2}+⋯.+V_{n}G_{n}))/(G_{1}+G_{2}+⋯G_{n})

d) V^{‘}=((V_{1}/G_{1}+V_{2}/G_{2}+⋯.+V_{n}/G_{n}))/( G_{1}+G_{2}+⋯G_{n})

2. According to Millman’s Theorem, if there are n voltage sources with n internal resistances respectively, are in parallel, then the value of equivalent resistance is?

a) R’=G_{1}+G_{2}+⋯G_{n}

b) R’=1/G_{1}+1/G_{2}+⋯1/G_{n}

c) R’=1/((G_{1}+G_{2}+⋯G_{n}))

d) R’=1/(1/G_{1}+1/G_{2}+⋯1/G_{n})

3. According to Millman’s Theorem, if there are n voltage sources with n internal resistances respectively, are in parallel, then these sources are replaced by?

a) single current source I’ in series with R’

b) single voltage source V’ in series with R’

c) single current source I’ in parallel to R’

d) single voltage source V’ in parallel to R’

4. According to Millman’s Theorem, if there are n current sources with n internal conductances respectively, are in series, then these sources are replaced by?

a) single voltage source V’ in parallel with G’

b) single current source I’ in series with G’

c) single current source I’ in parallel with G’

d) single voltage source V’ in series with G’

5. According to Millman’s Theorem, if there are n current sources with n internal conductances respectively, are in series, then the value of equivalent conductance is?

a) G’=R_{1}+R_{2}+⋯R_{n}

b) G’=1/(1/R_{1}+1/R_{2}+⋯1/R_{n})

c) G’=1/((R_{1}+R_{2}+⋯R_{n}))

d) G’=1/R_{1}+1/R_{2}+⋯1/R_{n}

6. Find the current through 3Ω resistor in the circuit shown below using Millman’s Theorem.

a) 4

b) 3

c) 2

d) 1

7. According to Millman’s Theorem, if there are n current sources with n internal conductances respectively, are in series, then the value of equivalent current source is?

a) I^{‘}=((I_{1}R_{1}+I_{2}R_{2}+⋯.+I_{n}R_{n}))/(R_{1}+R_{2}+⋯R_{n})

b) I’=I_{1}R_{1}+I_{2}R_{2}+⋯.+I_{n}R_{n}

c) I’=((I_{1}/R_{1}+I_{2}/R_{2}+⋯.+I_{n}/R_{n}))/(R_{1}+R_{2}+⋯R_{n})

d) I’=I_{1}/R_{1}+I_{2}/R_{2}+⋯.+I_{n}/R_{n}

8. Calculate the current through 3Ω resistor in the circuit shown below.

a) 1

b) 2

c) 3

d) 4

9. Consider the circuit shown below. Find the current through 4Ω resistor.

a) 2

b) 1.5

c) 1

d) 0.5

10. In the following circuit. Find the current through 4Ω resistor using Millman’s Theorem.

a) 0.5

b) 1

c) 1.5

d) 2