# Basics of Network Analysis

 Question 1
In the circuit shown below, the current $i$ flowing through $200 \Omega$ resistor is ____ $m A$ (rounded off to two decimal places).

 A 1.36 B 0.84 C 2.36 D 3.54
GATE EC 2023   Network Theory
Question 1 Explanation:
By applying source transformation,

Apply nodal at node $V_{A}$,
\begin{aligned} \frac{V_{A}-2}{2 \mathrm{k} \Omega}+\frac{V_{A}}{2 \mathrm{k} \Omega}+\frac{V_{A}+1}{1.2 \mathrm{k} \Omega} & =1 \mathrm{~mA} \\ V_{A}\left[\frac{1}{2}+\frac{1}{2}+\frac{1}{1.2}\right] & =1+\frac{2}{2}-\left(\frac{1}{1.2}\right) \\ V_{A} & =0.636 \mathrm{~V} \end{aligned}

The current through $200 \Omega$ resistor,
\begin{aligned} & i=\frac{V_{A}+1}{1.2 \mathrm{k} \Omega}=\frac{0.636+1}{1.2} \\ & i=1.36 \mathrm{~mA} \end{aligned}
 Question 2
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 2 Explanation:
Here, there is no any return closed path for Current (I) . Hence I=0
Current always flow in loop.

 Question 3
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 3 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 4
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 4 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 5
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 5 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}

There are 5 questions to complete.