The Circuit Shown Below, Let (A) Write a Node Equation at Node 1 by Summing

Essay

the circuit shown below, let $\mathrm { R } _ { 1 } = 1 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 4 \mathrm { k } \Omega , \mathrm { R } _ { \mathrm { i } } = 3 \mathrm { k } \Omega , \mathrm { R } _ { \mathrm { o } } = 2 \mathrm { k } \Omega , \mathrm { A } = 1000 , \mathrm { v } _ { \mathrm { s } } = 1 \mathrm {~V} , \mathrm { v } _ { \mathrm { p } } = \mathrm { v } _ { \mathrm { s } }$
(a) Write a node equation at node 1 by summing currents away from node 1 .
(b) Write a node equation at node 2 by summing currents away from node 2 .
(c) Solve the two node equations to find numerical values of $v _ { n }$ and $v _ { o }$ .
(d) Find the value of $i _ { s }$ through $R _ { i }$ . Find the input impedance $R _ { i n } = v _ { s } / i _ { s }$ .