Question 1

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

Accepted Answer

$$\begin{array} { l } 
- I _ { s } + \frac { V _ { 1 } - V _ { s } } { R _ { 1 } } + \frac { V _ { 1 } - V _ { 2 } } { R _ { 2 } } + \frac { V _ { 1 } } { R _ { 4 } } = 0 \
\frac { V _ { 2 } - V _ { 1 } } { R _ { 2 } } + \frac { V _ { 2 } } { R _ { 3 } } + \frac { V _ { 2 } - V _ { s } } { R _ { 3 } } = 0 \
V _ { 1 } = 4.9367 \mathrm {~V} , V _ { 2 } = 3.4684 \mathrm {~V}
\end{array}$$ % 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: $$\begin{array} { l } 
\mathrm { V } 1 = \
4.936709 \
\mathrm {~V} = \
3.468354
\end{array}$$

Question 2

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) Find $V _ { 1 }$ and $V _ { 2 }$ by solving the two node equations.
(d) Find the currents $\mathrm { I } _ { \mathrm { R } 1 } , \mathrm { I } _ { \mathrm { R } 2 } , \mathrm { I } _ { \mathrm { R } 3 } , \mathrm { I } _ { \mathrm { R } 4 } , \mathrm { I } _ { 5 }$.
(e) Find the power absorbed by $\mathrm { R } _ { 1 } , \mathrm { R } _ { 2 } , \mathrm { R } _ { 3 } , \mathrm { R } _ { 4 }$, and power released by $\mathrm { V } _ { \mathrm { s } }$ and $\mathrm { I } _ { \mathrm { s } }$.

Accepted Answer

$$\begin{array} { l } 
- I _ { s } + \frac { V _ { 1 } - V _ { s } } { R _ { 1 } } + \frac { V _ { 1 } - V _ { 2 } } { R _ { 2 } } + \frac { V _ { 1 } } { R _ { 4 } } = 0 \
\frac { V _ { 2 } - V _ { 1 } } { R _ { 2 } } + \frac { V _ { 2 } } { R _ { 5 } } + \frac { V _ { 2 } - V _ { s } } { R _ { 3 } } = 0 \
\mathrm {~V} _ { 1 } = 12 \mathrm {~V} , \mathrm {~V} _ { 2 } = 6 \mathrm {~V}
\end{array}$$ % Nodal Analysis clear all;
$R 1 = 2000 ; R 2 = 3000 ; \mathrm { R } 3 = 500 ; \mathrm { R } 4 = 1000 ;$
$R 1 = 2000 ; R 2 = 3000 ; R 3 = 500 ; R 4 = 1000$
$\mathrm { Vs } = 8 ; \mathrm { Ig } = 4 \mathrm { e } - 3 ;$ \[\begin{array}{l}
\text { syms } \mathrm { V } 1 \text { V2 }\
[ V 1 , V 2 ] = s o l v e ( - I s + ( V 1 - V s ) / R 1 + ( V 1 - V 2 ) / R 2 , \ldots\
( V 2 - V 1 ) / R 2 + V 2 / R 4 + ( V 2 - V s ) / R 3 , V 1 , V 2 ) \text {; }\
\mathrm { IR } 1 = ( \mathrm { Vl } - \mathrm { Vs } ) / \mathrm { Rl } \text {; }\
I R 2 = ( V 1 - V 2 ) / R 2 \text {; }\
I R 3 = ( V s - V 2 ) / R 3 \text {; }\
\text { I } R 4 = V 2 / R 4 \text {; }\
\text { I } 5 = \text { IR3-IRI; }\
\mathrm { PRI } = \mathrm { IRl } { } ^ { \wedge } 2 \text { * } \mathrm { R } 1 \text {; }\
\mathrm { PR } 2 = \mathrm { IR } 2 ^ { \wedge } 2 * \mathrm { R } 2 \text {; }\
\mathrm { PR } 3 = \mathrm { IR } 3 \wedge 2 * \mathrm { R } 3 \text {; }\
\mathrm { PR } 4 = \operatorname { IR } 4 { } ^ { \wedge } 2 ^ { * } \mathrm { R } 4 \text {; }\
\text { PVs } = - I 5 ^ { * } \mathrm { Vs } \text {; }\
\text { PIs } = - I s * V 1 \text {; }\
\mathrm { Pa } = \mathrm { PR } 1 + \mathrm { PR } 2 + \mathrm { PR } 3 + \mathrm { PR } 4 \text {; }\
\mathrm { Ps } = \mathrm { PVs } + \mathrm { PIs } \text {; }\
\text { Psum=PR1 +PR2 +PR3+PR4+PVs+PIs; }\
V 1 = \operatorname { vpa } ( \mathrm { V } 1,7 )\
\mathrm { V } 2 = \mathrm { vpa } ( \mathrm { V } 2,7 )\
\text { IR } 1 = \text { vpa (IR1, } 7 )\
\text { IR2=vpa (IR2, 7) }\
\text { IR3=vpa (IR3, } 7 )\
\text { IR4=vpa (IR4, 7) }\
15 \text {-vpa } ( 15,7 )\
\mathrm { PR } 1 = \mathrm { vpa } ( \mathrm { PR } 1,7 )\
\text { PR2-vpa (PR2, 7) }\
\text { PR3 =vpa } ( \text { PR3, } 7 )\
\text { PR4 =vpa } ( \mathrm { PR } 4,7 )\
\text { PVs=vpa } ( \mathrm { PVs } , 7 )\
\text { PIs=vpa (PIs, } 7 \text { ) }\
\mathrm { Pa } = \mathrm { vpa } ( \mathrm { Pa } , 7 )\
\text { Ps=vpa } ( \mathrm { Ps } , 7 )\
\text { Psum=vpa } \{ \text { Psum, 7) }
\end{array}\] Answers: $$\begin{array} { l } 
\mathrm { V } 1 = \
12.0 \
\mathrm {~V} 2 = \
6.0 \
\text { IR1 = } \
0.002 \
\text { IR2 = } \
0.002 \
\text { IR3 = } \
0.004 \
\text { IR4= } \
0.006 \
\text { I5 = } \
0.002 \
\text { PR1 = } \
0.008 \
\text { PR2 = } \
0.012 \
\text { PR3 = } \
0.008 \
\text { PR4 = } \
0.036 \
\text { PVs = } \
- 0.016 \
\text { PIs = } \
- 0.048 \
\text { Pa = } \
0.064 \
\text { Ps = } \
- 0.064 \
\text { Psum = } \
0.0
\end{array}$$

Question 3

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 $V _ { 2 }$.

Accepted Answer

$$\begin{array} { l } 
- V _ { \mathrm { s } } + \mathrm { R } _ { 1 } \mathrm { I } _ { 1 } + \mathrm { R } _ { 3 } \left( \mathrm { I } _ { 1 } - \mathrm { I } _ { 2 } \right) = 0 \
\mathrm { I } _ { 2 } = - \mathrm { g } _ { \mathrm { m } } \mathrm { V } _ { 1 } \
\mathrm {~V} _ { 1 } = \mathrm { R } _ { 3 } \left( \mathrm { I } _ { 1 } - \mathrm { I } _ { 2 } \right) \
\mathrm { V } _ { 2 } = \mathrm { V } _ { 1 } - \mathrm { R } _ { 2 } \mathrm { I } _ { 2 } \
\mathrm { I } _ { 1 } = 1.4 \mathrm {~mA} , \mathrm { I } _ { 2 } = - 1.4 \mathrm {~mA} , \mathrm {~V} _ { 1 } = 2.8 \mathrm {~V} , \mathrm {~V} _ { 2 } = 6.3 \mathrm {~V}
\end{array}$$ % 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 $( - V s + R 1 * I 1 + R 3 * ( I 1 - I 2 ) , I 2 = = - g m * R 3 * ( I 1 - I 2 ) , I 1 , I 2 )$
$V 1 = R 3 ^ { * } ( I 1 - I 2 )$
$\mathrm { V } 2 = \mathrm { V } 1 - \mathrm { R } 2 ^ { * } \mathrm { I } 2$
$I I = \operatorname { Vpa } ( I 1,7 )$ $$\begin{array} { l } 
I 2 = \mathrm { vpa } ( I 2,7 ) \
\mathrm { V } 1 = \mathrm { vpa } ( \mathrm { V } 1,7 ) \
\mathrm { V } 2 = \mathrm { vpa } ( \mathrm { V } 2,7 ) \
\text { Answers: } \
\mathrm { I } 1 = \
0.0014 \
\mathrm { I } 2 = \
- 0.0014 \
\mathrm {~V} 1 = \
2.8 \
\mathrm {~V} 2 = \
6.3
\end{array}$$

Question 4

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

Accepted Answer

The answer of the circuit shown below, let \[\mathrm {...

Question 5

In the circuit shown below, let $$\mathrm { V } _ { \mathrm { s } } = 9 \mathrm {~V} , \mathrm { R } _ { 1 } = 1 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 400 \Omega , \mathrm { R } _ { 3 } = 500 \Omega , \mathrm { R } _ { 4 } = 1.2 \mathrm { k } \Omega , \mathrm { g } _ { \mathrm { m } } = 0.0004$$
Use mesh analysis to find mesh currents $I _ { 1 } , I _ { 2 }$, and $I _ { 3 }$. Also, find $V _ { 1 }$ and $V _ { 2 }$.

Accepted Answer

The answer of In the circuit shown below, let \[\mathrm...

Question 6

the circuit shown below, $$\text { (a) Write a node equation at node } 1 \text { by summing the currents away from node } 1 .$$ (b) Write a node equation at node 2 by summing the currents away from node $2 .$
(c) Solve the equations to find $V _ { 1 }$ and $V _ { 2 }$.
(d) Find the current through $\mathrm { R } _ { 1 }$ (including direction) and power dissipated on $\mathrm { R } _ { 1 }$.

Accepted Answer

The answer of the circuit shown below, \[\text { (a)...

Question 7

In the circuit shown below, let $$\mathrm { V } _ { \mathrm { s } } = 7 \mathrm {~V} , \mathrm { I } _ { \mathrm { s } } = 2 \mathrm {~mA} , \mathrm { R } _ { 1 } = 1 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 1.5 \mathrm { k } \Omega , \mathrm { R } _ { 3 } = 5 \mathrm { k } \Omega , \mathrm { R } _ { 4 } = 500 \Omega$$
Use mesh analysis to find mesh currents $I _ { 1 } , I _ { 2 }$, and $I _ { 3 }$. Also, find $V _ { 1 }$ and $V _ { 2 }$.

Accepted Answer

The answer of In the circuit shown below, let \[\mathrm...

Question 8

In the circuit shown below, let $I _ { \mathrm { s } 1 } = 5 \mathrm {~mA} , \mathrm { I } _ { \mathrm { s } 2 } = 2 \mathrm {~mA} , \mathrm { R } _ { 1 } = 1 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 500 \Omega , \mathrm { R } _ { 3 } = 1.5 \mathrm { k } \Omega , \mathrm { R } _ { 4 } = 600 \Omega$.
Use mesh analysis to find mesh currents $\mathrm { I } _ { 1 } , \mathrm { I } _ { 2 }$, and $\mathrm { I } _ { 3 }$. Also, find $\mathrm { V } _ { 1 } , \mathrm {~V} _ { 2 }$, and $\mathrm { V } _ { 3 }$.

Accepted Answer

The answer of In the circuit shown below, let \(I...

Question 9

In the circuit shown below, let $V _ { s } = 8 V , I _ { s } = 2 \mathrm {~mA} , R _ { 1 } = 1 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 400 \Omega , \mathrm { R } _ { 3 } = 1.5 \mathrm { k } \Omega , \mathrm { R } _ { 4 } = 2.5 \mathrm { k } \Omega , \mathrm { R } _ { 5 } = 600 \Omega$
Use mesh analysis to find mesh currents $\mathrm { I } _ { 1 } , \mathrm { I } _ { 2 }$, and $\mathrm { I } _ { 3 }$. Also, find $\mathrm { V } _ { 1 } , \mathrm {~V} _ { 2 }$, and $\mathrm { V } _ { 3 }$.

Accepted Answer

The answer of In the circuit shown below, let \(V...

Question 10

the circuit shown below, let $$V _ { \mathrm { s } 1 } = 6 \mathrm {~V} , \mathrm {~V} _ { \mathrm { s } 2 } = 1 \mathrm {~V} , \mathrm { R } _ { 1 } = 1 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 1.5 \mathrm { k } \Omega , \mathrm { R } _ { 3 } = 2.5 \mathrm { k } \Omega , \mathrm { R } _ { 4 } = 1.2 \mathrm { k } \Omega , \mathrm { R } _ { 5 } = 800 \Omega$$
Use nodal analysis to find $V _ { 1 } , V _ { 2 }$, and $V _ { 3 }$.

Accepted Answer

The answer of the circuit shown below, let \[V _...

Question 11

In the circuit shown below, let $\mathrm { V } _ { \mathrm { s } } = 3 \mathrm {~V} , \mathrm { R } _ { 1 } = 3 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 1.5 \mathrm { k } \Omega , \mathrm { R } _ { 3 } = 1 \mathrm { k } \Omega , \mathrm { R } _ { 4 } = 1.2 \mathrm { k } \Omega$
Use nodal analysis to find $V _ { 1 }$ and $V _ { 2 }$.

Accepted Answer

The answer of In the circuit shown below, let \(\mathrm...

Question 12

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

Accepted Answer

The answer of the circuit shown below, let \[\mathrm {...

Question 13

In the circuit shown below, (a) Write a mesh equation by summing the voltage drops around mesh 1 (left side).
(b) Write a mesh equation by summing the voltage drops around mesh 2 (right side).
(c) Solve the two equations to find $I _ { 1 }$ and $I _ { 2 }$.
(d) Find voltage $V _ { 3 }$ across $R _ { 2 }$.

Accepted Answer

The answer of In the circuit shown below, (a) Write...

Question 14

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

Accepted Answer

The answer of the circuit shown below, let \[\mathrm {...

Question 15

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

Accepted Answer

The answer of In the circuit shown below, let \(\mathrm...

Question 16

In the circuit shown below, (a) Write a mesh equation around mesh 1 by summing the voltage drops around mesh 1 .
(b) Write a mesh equation around supermesh formed by meshes 2 and 3 by summing the voltage drops around supermesh.
(c) Write a constraint equation expressing $\mathrm { I } _ { \mathrm { s } }$ by $\mathrm { I } _ { 2 }$ and $\mathrm { I } _ { 3 }$.
(d) Find $\mathrm { I } _ { 1 } , \mathrm { I } _ { 2 }$, and $\mathrm { I } _ { 3 }$ by solving the three equations.
(e) Find the voltages $V _ { 1 } , V _ { 2 }$.

Accepted Answer

The answer of In the circuit shown below, (a) Write...

Question 17

the circuit shown below, let $V _ { s 1 } = 7 V , V _ { s 2 } = 1 V , R _ { 1 } = 2 \mathrm { k } \Omega , R _ { 2 } = 1.2 \mathrm { k } \Omega , R _ { 3 } = 2.2 \mathrm { k } \Omega , R _ { 4 } = 1.5 \mathrm { k } \Omega , R _ { 5 } = 800 \Omega , R _ { 6 } = 500$ $\Omega$.
Use nodal analysis to find $V _ { 1 } , V _ { 2 }$, and $V _ { 3 }$.

Accepted Answer

The answer of the circuit shown below, let \(V _...

Question 18

In the circuit shown below, let $$V _ { \mathrm { s } } = 5 \mathrm {~V} , \mathrm { I } _ { \mathrm { s } } = 2 \mathrm {~mA} , \mathrm { R } _ { 1 } = 1 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 400 \Omega , \mathrm { R } _ { 3 } = 1.5 \mathrm { k } \Omega , \mathrm { R } _ { 4 } = 2 \mathrm { k } \Omega , \mathrm { R } _ { 5 } = 500 \Omega$$
Use mesh analysis to find mesh currents $I _ { 1 } , I _ { 2 }$, and $I _ { 3 }$. Also, find $V _ { 1 } , V _ { 2 }$, and $V _ { 3 }$.

Accepted Answer

The answer of In the circuit shown below, let \[V...

Question 19

In the circuit shown below, let $$V _ { s } = 10 V , R _ { 1 } = 1 \mathrm { k } \Omega , R _ { 2 } = 500 \Omega , R _ { 3 } = 600 \Omega , R _ { 4 } = 800 \Omega , R _ { 5 } = 400 \Omega , k = 0.2 , g _ { m } = 0.0004$$
Use mesh analysis to find mesh currents $\mathrm { I } _ { 1 } , \mathrm { I } _ { 2 } , \mathrm { I } _ { 3 }$, and $\mathrm { I } _ { 4 }$. Also, find $\mathrm { V } _ { 1 } , \mathrm {~V} _ { 2 }$, and $\mathrm { V } _ { 3 }$.

Accepted Answer

The answer of In the circuit shown below, let \[V...

Question 20

the circuit shown below, let $$V _ { \mathrm { s } } = 5 V , R _ { 1 } = 3 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 2 \mathrm { k } \Omega , \mathrm { R } _ { 3 } = 5 \mathrm { k } \Omega , \mathrm { R } _ { 4 } = 1 \mathrm { k } \Omega , \mathrm { g } _ { \mathrm { m } } = 0.0005$$
(a) Write a node equation at node 1 by summing the currents away from node 1 .
(b) Write a node equation at node 2 by summing the currents away from node 2 .
(c) Solve the equations to find $V _ { 1 }$ and $V _ { 2 }$.
(d) Find the current through $\mathrm { R } _ { 4 }$ (including direction) and power absorbed by $\mathrm { R } _ { 4 }$.

Accepted Answer

The answer of the circuit shown below, let \[V _...

Quiz 3: Circuit Analysis Methods