# Basics of Network Analysis

 Question 1
Consider the circuit shown in the figure. The current $I$ flowing through the $10\Omega$ resistor is _________.

 A 1A B 0A C 0.1A D -0.1A
GATE EC 2022   Network Theory
Question 1 Explanation:
Here, there is no any return closed path for Current (I) . Hence I=0
Current always flow in loop.
 Question 2
The current $I$ in the circuit shown is ________

 A $1.25 \times 10^{-3}A$ B $0.75 \times 10^{-3}A$ C $-0.5 \times 10^{-3}A$ D $1.16 \times 10^{-3}A$
GATE EC 2022   Network Theory
Question 2 Explanation:

Applying Nodal equation at Node-A
\begin{aligned} \frac{V_A}{2k}+\frac{V_A-5}{2k}&=10^{-3}\\ \Rightarrow 2V_A-5&=2k \times 10^{-3}\\ V_A&=3.5V\\ Again,&\\ I&=\frac{5-V_A}{2k}\\ &=\frac{5-3.5}{2k}\\ &=0.75 \times 10^{-3}A \end{aligned}
 Question 3
Consider the circuit shown in the figure.

The value of $v_{0}$ (rounded off to one decimal place) is _________ V.
 A 0.5 B 0.8 C 2 D 1
GATE EC 2021   Network Theory
Question 3 Explanation:

Write KVL equation first loop,
\begin{aligned} V_{o}-4+1\left(V_{o}+2\right) &=0 \\ V_{o} &=1 \mathrm{~V} \end{aligned}
 Question 4
Consider the circuit shown in the figure.

The current I flowing through the $7\:\Omega$ resistor between P and Q (rounded off to one decimal place) is ________ A.
 A 0.2 B 0.5 C 0.8 D 1.4
GATE EC 2021   Network Theory
Question 4 Explanation:
Redraw the circuit,
\begin{aligned} 3 \Omega \;||\; 6 \Omega&=2 \Omega \\ 2 \Omega \;||\; 2 \Omega&=1 \Omega \\ \qquad I&=5 \times \frac{1}{10}=0.5 \mathrm{~A} \end{aligned}

 Question 5
The current I in the given network is
 A 0 A B $2.38 \angle -96.37^{\circ}$ A C $2.38 \angle 143.63^{\circ}$ A D $2.38 \angle -23.63^{\circ}$ A
GATE EC 2020   Network Theory
Question 5 Explanation:

$I=-[I_{1}+I_{2}]$
$I=-\left [ \frac{120\angle -90^{\circ}}{80-j35}+\frac{120\angle -30^{\circ}}{80-j35} \right ]$
$I=2.38\angle 143.7^{\circ}$
 Question 6
Consider the network shown below with $R_{1} = 1\Omega , R_{2} = 2\Omega \; and \; R_{3} = 3\Omega$. The network is connected to a constant voltage source of 11V.

The magnitude of the current (in amperes, accurate to two decimal places) through the source is _______.
 A 5 B 8 C 8.7 D 9.5
GATE EC 2018   Network Theory
Question 6 Explanation:

As the network is symmetric,
$V_{A}= V_{B} and V_{C}= V_{D}$
So current throught $R_{2}$ resistor is zero and $V_{A}=V_{B}$ and $V_{C}$=$V_{D}$,electrically the circuit can reduced as,

Total resistance,
\begin{aligned} R_{T} &=2\left(R_{1} \| R_{1}\right)+\left(R_{1}\left\|R_{1}\right\| R_{3} \| R_{3}\right) \\ &=R_{1}+\left(\frac{R_{1}}{2} \| \frac{R_{3}}{2}\right) \end{aligned}
Given that, $R_{1}=1 \Omega$ and $R_{3}=3 \Omega$
\begin{aligned} \text{So,}\qquad R_{T} &=1+\left(\frac{1}{2} \| \frac{3}{2}\right) \Omega=1+\frac{3 / 2}{4}=\frac{11}{8} \Omega \\ I &=\frac{11 \mathrm{V}}{R_{T}}=\frac{11}{(11 / 8)}=8 \mathrm{A} \end{aligned}
 Question 7
A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value 10$\Omega$, 5$\Omega$, 2$\Omega$ are provided. Consider all possible permutations of the given resistors into the positions A, B, C, and identify the configurations with maximum possible overall resistance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is ____________.
 A 0.466 B 2.14 C 16.758 D 6.098
GATE EC 2017-SET-2   Network Theory
Question 7 Explanation:
The connection of resistors is as shown below:

Given resistor values are :$10 \Omega, 5 \Omega, 2 \Omega$
The maximum resistance possible is,
\begin{aligned} R_{T(\max )} &=10 \Omega+(5 \Omega \| 2 \Omega) \\ &=\left(10+\frac{10}{7}\right) \Omega=\frac{80}{7} \Omega \end{aligned}
The minimum resistance possible is,
\begin{aligned} R_{T(\min )} &=2 \Omega+(10 \Omega \| 5 \Omega) \\ &=\left(2+\frac{10}{3}\right) \Omega=\frac{16}{3} \Omega \\ \frac{R_{T(\max )}}{R_{T(\min )}} &=\frac{80 / 7}{16 / 3}=\frac{15}{7}=2.143 \end{aligned}
 Question 8
In the figure shown, the current i (in ampere) is __________
 A 0 B -1 C -2 D -4
GATE EC 2016-SET-3   Network Theory
Question 8 Explanation:

Using KCL at $V_{1}$
$\frac{V_{1}}{1}+\frac{V_{1}-8}{1}+\frac{V_{1}-8}{1}+\frac{V_{1}}{1}=0$
or $V_{1}=4 V$
considering KVL, we get

 Question 9
In the circuit shown in the figure, the magnitude of the current (in amperes) through $R_{2}$ is ___
 A 2 B 3 C 4 D 5
GATE EC 2016-SET-2   Network Theory
Question 9 Explanation:

Using KVL in the outer loop
$60-5\left(0.16 V_{x}\right)-\frac{V_{x}}{5} \times 3-V_{x}=0$
$\text{or}\quad v_{x}=25 \mathrm{V}$
$\therefore$ The current flowing through
$R_{2}=\frac{V_{x}}{5}=\frac{25}{5}=5 \mathrm{A}$
 Question 10
In the given circuit, each resistor has a value equal to 1 $\Omega$.

What is the equivalent resistance across the terminals a and b?
 A 1/6 $\Omega$ B 1/3 $\Omega$ C 9/20 $\Omega$ D 8/15 $\Omega$
GATE EC 2016-SET-2   Network Theory
Question 10 Explanation:
$R_{eq}\Rightarrow$

By using delta to star conversion

Again by star to delta conversion

\begin{aligned} R_{\mathrm{ab}} &=\{4 \| 1)+(4 \| 1)\}\|\{1 \| 4)\} \\ &=\left(\frac{4}{5}+\frac{4}{5}\right) \| \frac{4}{5}=\frac{8}{15} \Omega \end{aligned}
There are 10 questions to complete.