In the circuit shown below, (a) Write a node equation at node 1 by summing the currents leaving node $1 .$
(b) Write a node equation at node 2 by summing the currents leaving node 2 .
(c) Solve the node equations to find the Thévenin equivalent voltage between $a$ and $b$, $\mathrm { V } _ { \text {th } } = \mathrm { V } _ { 2 }$.
(d) Find the Thévenin equivalent resistance Ruth between $a$ and $b$.
(e) Find the load resistance R. between $a$ and $b$ for the maximum power transfer to the load. Also, find the maximum power delivered to the load.

Question

Quizplus · Accepted Answer

The Answer is

\frac { V _ { 1 } - V _ { s } } { R _ { 2 } } - I _ { s } + \frac { V _ { 1 } - V _ { 2 } } { R _ { 3 } } = 0

\begin{array} { l } \frac { V _ { 2 } - V _ { s } } { R _ { 1 } } + \frac { V _ { 2 } - V _ { 1 } } { R _ { 3 } } + \frac { V _ { 2 } } { R _ { 4 } } = 0 \\mathrm {~V} _ { 1 } = 16.6667 \mathrm {~V} , \mathrm {~V} _ { ext {th } } = \mathrm { V } _ { 2 } = 14 \mathrm {~V} \\mathrm { R } _ { \mathrm { th } } = \mathrm { R } _ { 4 } \left\| \left( \mathrm { R } _ { 2 } + \mathrm { R } _ { 3 } ight) ight\| \mathrm { R } _ { 1 } = 1.05 \mathrm { k } \Omega \\mathrm { R } _ { \mathrm { L } } = \mathrm { R } _ { \mathrm { th } } = 1.05 \mathrm { k } \Omega \p _ { L } = \frac { V _ { t h } ^ { 2 } } { 4 R _ { t h } } = 46.6667 \mathrm {~mW}\end{array}

clear all;

\mathrm { R } 1 = 3000 ; \mathrm { R } 2 - 2000 ; \mathrm { R } 3 - 1000 ; \mathrm { R } 4 = 3500 ; \mathrm { Vs } = 18 ; \mathrm { I } s = 0.002

;

R a = P ( [ R 1 , R 2 + R 3 ] )

Rth

= \mathrm { P } ( [ \mathrm { Ra } , \mathrm { R } 4 ] )

syms V1 V2

[ \mathrm { V } 1 , \mathrm {~V} 2 ] = \mathrm { sol } \mathrm { Ve } ( \langle \mathrm { V } 1 - \mathrm { Vs } ) / \mathrm { R } 2 - \mathrm { Is } + ( \mathrm { V } 1 - \mathrm { V } 2 ) / \mathrm { R } 3 , \ldots

( \mathrm { V } 2 - \mathrm { Vs } ) / \mathrm { R } 1 + ( \mathrm { V } 2 - \mathrm { V } 1 ) / \mathrm { R } 3 + \mathrm { V } 2 / \mathrm { R } 4 , \mathrm {~V} 1 , \mathrm {~V} 2 )

;

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

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

\mathrm { Vth } = \mathrm { V } 2

RL=Rth

\mathrm { P } = \mathrm { V } \operatorname { th } ^ { \wedge } 2 / \left( 4 { } ^ { \star } \mathrm { Rth } ight)

Answers:

\begin{array} { l } ext { Raz } = 1500 \ ext { Rth } =1050 \V 1 = \16.66667 \ ext { V2 = } \14.0 \ ext { Vth } = \14.0 \ ext { RL } = 1050\ ext { P } = \0.046666666666666666666666666666667\end{array}

In the Circuit Shown Below, (A) Write a Node Equation 1.1 .1.

In the Circuit Shown Below, (A) Write a Node Equation $1 .$