the circuit shown below, let $$\mathrm { I } _ { \mathrm { s } } = 2 \mathrm {~mA} , \mathrm {~V} _ { \mathrm { s } } = 6 \mathrm {~V} , \mathrm { R } _ { 1 } = 1.5 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 2 \mathrm { k } \Omega , \mathrm { R } _ { 3 } = 6 \mathrm { k } \Omega , \mathrm { R } _ { 4 } = 2.5 \mathrm { k } \Omega , \mathrm { R } _ { 5 } = 3 \mathrm { k } \Omega$$ $$\text { Use nodal analysis to find } V _ { 1 } \text { and } V _ { 2 } \text {. }$$

Question

Quizplus · Accepted Answer

The Answer is

\begin{array} { l } - I _ { s } + \frac { V _ { 1 } - V _ { s } } { R _ { 1 } } + \frac { V _ { 1 } - V _ { 2 } } { R _ { 2 } } + \frac { V _ { 1 } } { R _ { 4 } } = 0 \\frac { V _ { 2 } - V _ { 1 } } { R _ { 2 } } + \frac { V _ { 2 } } { R _ { 3 } } + \frac { V _ { 2 } - V _ { s } } { R _ { 3 } } = 0 \V _ { 1 } = 4.9367 \mathrm {~V} , V _ { 2 } = 3.4684 \mathrm {~V}\end{array}

% Nodal Analysis clear all;
Is

= 0.002 ; \mathrm { Vs } = 6 ;

R 1 = 1500 ; R 2 = 2000 ; R 3 = 6000 , R 4 = 2500 ; R 5 = 3000

;
syms V1 V2

[ \mathrm { V } 1 , \mathrm {~V} 2 ] =

solve

( - \mathrm { Is } + \mathrm { V } 1 / \mathrm { R } 4 + ( \mathrm { V } ] - \mathrm { Vs } ) / \mathrm { R } 1 + ( \mathrm { V } 1 - \mathrm { V } 2 ) / \mathrm { R } 2 , \ldots

( \mathrm { V } 2 - \mathrm { V } 1 ) / \mathrm { R } 2 + \mathrm { V } 2 / \mathrm { R } 5 + ( \mathrm { V } 2 - \mathrm { Vs } ) / \mathrm { R } 3 , \mathrm {~V} 1 , \mathrm {~V} 2 )

;

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

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

I 4 - V 1 / R 4

I 2 = ( V 1 - V 2 ) / R 2

I 1 = ( V s - V 1 ) / R 1

I 3 = ( \mathrm { Vs } - \mathrm { V } 2 ) / \mathrm { R } 3

I S = V 2 / R 5

IVs-I4+I5-Is

I l a = - I 3 + I V

s Answers:

\begin{array} { l } \mathrm { V } 1 = \4.936709 \\mathrm {~V} = \3.468354\end{array}

The Circuit Shown Below, Let Use nodal analysis to find V1 and V2. \text { Use nodal analysis to find } V _ { 1 } \text { and } V _ { 2 } \text {. } Use nodal analysis to find V1​ and V2​.

The Circuit Shown Below, Let $\text { Use nodal analysis to find } V _ { 1 } \text { and } V _ { 2 } \text {. }$