In the Circuit Shown Below, LetUse Mesh Analysis to Find Mesh Currents

Question

Examlex · Accepted Answer

The Answer is

\begin{array} { l } \mathrm { R } _ { 1 } \mathrm { I } _ { 1 } + \mathrm { R } _ { 4 } \mathrm { I } _ { 3 } + \mathrm { R } _ { 3 } \left( \mathrm { I } _ { 3 } - \mathrm { I } _ { 2 } ight) + \mathrm { R } _ { 2 } \left( \mathrm { I } _ { 1 } - \mathrm { I } _ { 2 } ight) = 0 \- \mathrm { V } _ { \mathrm { s } } + \mathrm { R } _ { 2 } \left( \mathrm { I } _ { 2 } - \mathrm { I } _ { 1 } ight) + \mathrm { R } _ { 3 } \left( \mathrm { I } _ { 2 } - \mathrm { I } _ { 3 } ight) = 0 \\mathrm { I } _ { 3 } - \mathrm { I } _ { 1 } = \mathrm { g } _ { \mathrm { m } } \mathrm { V } _ { 1 } \\mathrm {~V} _ { 1 } = \mathrm { R } _ { 3 } \left( \mathrm { I } _ { 2 } - \mathrm { I } _ { 3 } ight) \\mathrm { V } _ { 2 } = \mathrm { R } _ { 4 } \mathrm { I } _ { 3 } \\mathrm { I } _ { 1 } = 3.0891 \mathrm {~mA} , \mathrm { I } _ { 2 } = 14.1095 \mathrm {~mA} , \mathrm { I } _ { 3 } = 4.9258 \mathrm {~mA} , \mathrm {~V} _ { 1 } = 4.5918 \mathrm {~V} , \mathrm {~V} _ { 2 } = 5.9109 \mathrm {~V}\end{array}

% Mesh Analysis clear all

V S = 9 ;

R 1 = 1000 ; R 2 = 400 ; R 3 = 500 ; R 4 = 1200 ; g m = 0.0004

syms I1 I2 I3

[ I 1 , I 2 , I 3 ] - s 0 l v e ( - V s + R 2 * ( I 2 - I 1 ) + R 3 * ( I 2 - I 3 ) , \ldots

R 1 * I 1 + R 4 ^ { * } I 3 + R 3 ^ { * } \{ I 3 - I 2 ) + R 2 ^ { * } ( I I - I 2 ) , \ldots

\left. I 3 - I 1 = = g _ { m } * R 3 * ( I 2 - I 3 ) , I 1 , I 2 , I 3 ight)

V 1 = R 3 ^ { * } ( I 2 - I 3 )

\mathrm { V } 2 = \mathrm { R } 4 ^ { * } \mathrm { I } 3

IR

4 = I 3

IRl

= \mathrm { Il }

IR2

= I 2 - I 1

IR

3 = I 2 = I 3

SumI

= - I R 2 + I R 3 + g m * v 1

I 1 = \operatorname { vpa } ( I 1,7 )

I 2 = \operatorname { vpa } ( I 2,7 )

I

3 = \operatorname { vpa } ( I 3,7 )

V 1 = \operatorname { vpa } ( \mathrm { V } 1,7 )

\mathrm { V } 2 = \mathrm { Vpa } ( \mathrm { V } 2,7 )

\operatorname { IR4 } = \mathrm { vpa } ( \operatorname { IR4 } , 7 )

IR1=Vpa (IR1, 7)
IR2 = VPa (IR2, 7)
IR3=vpa

( \operatorname { IR3 } , 7 )

SumI=vpa

(

SumI,

7 )

Answers:

\begin{array} { l } I 1 = \0.003089054 \I 2 = \0.01410946 \I 3 = \0.004925788 \V 1 = \4.591837 \V 2 = \5.910946\end{array}

In the Circuit Shown Below, Let Use Mesh Analysis to Find Mesh Currents