In the circuit shown below, let $$\mathrm { V } _ { \mathrm { s } } = 7 \mathrm {~V} , \mathrm { R } _ { 1 } = 3 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 2.5 \mathrm { k } \Omega , \mathrm { R } _ { 3 } = 1 \mathrm { k } \Omega , \mathrm { g } _ { \mathrm { m } } = 0.0005$$
Use mesh analysis to find mesh currents $I _ { 1 }$ and $I _ { 2 }$. Also, find $V _ { 1 }$ and $V _ { 2 }$.

Question

Quizplus · Accepted Answer

The Answer is

\begin{array} { l } - V _ { \mathrm { s } } + \mathrm { R } _ { 1 } \mathrm { I } _ { 1 } + \mathrm { R } _ { 3 } \left( \mathrm { I } _ { 1 } - \mathrm { I } _ { 2 } ight) = 0 \\mathrm { I } _ { 2 } = - \mathrm { g } _ { \mathrm { m } } \mathrm { V } _ { 1 } \\mathrm {~V} _ { 1 } = \mathrm { R } _ { 3 } \left( \mathrm { I } _ { 1 } - \mathrm { I } _ { 2 } ight) \\mathrm { V } _ { 2 } = \mathrm { V } _ { 1 } - \mathrm { R } _ { 2 } \mathrm { I } _ { 2 } \\mathrm { I } _ { 1 } = 1.4 \mathrm {~mA} , \mathrm { I } _ { 2 } = - 1.4 \mathrm {~mA} , \mathrm {~V} _ { 1 } = 2.8 \mathrm {~V} , \mathrm {~V} _ { 2 } = 6.3 \mathrm {~V}\end{array}

% Mesh Analysis clear all

\mathrm { Vs } = 7

;

\mathrm { R } 1 = 3000 ; \mathrm { R } 2 = 2500 ; \mathrm { R } 3 = 1000 ; \mathrm { gm } = 0.0005 ;

clear all

V s = 7 ;

R

1 = 3000 ; R 2 = 2500 ; R 3 = 1000 ; g m = 0.0005 ;

syms Il I2

[ I 1 , I 2 ] =

solve

( - V s + R 1 * I 1 + R 3 * ( I 1 - I 2 ) , I 2 = = - g m * R 3 * ( I 1 - I 2 ) , I 1 , I 2 )

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

\mathrm { V } 2 = \mathrm { V } 1 - \mathrm { R } 2 ^ { * } \mathrm { I } 2

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

\begin{array} { l } I 2 = \mathrm { vpa } ( I 2,7 ) \\mathrm { V } 1 = \mathrm { vpa } ( \mathrm { V } 1,7 ) \\mathrm { V } 2 = \mathrm { vpa } ( \mathrm { V } 2,7 ) \ ext { Answers: } \\mathrm { I } 1 = \0.0014 \\mathrm { I } 2 = \- 0.0014 \\mathrm {~V} 1 = \2.8 \\mathrm {~V} 2 = \6.3\end{array}

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