GATE stands for Graduate Aptitude Test in Engineering. GATE stands as an significant milestone for countless aspiring engineers who are willing to seek admission to postgraduate programs or pursuing career opportunities in the field of engineering.

For clearing gate, you have to prepare subjects like Network, Electrical measurements, Engineering Mathematics, Signals and System, Electrical Machines, Power System, and many more.

You may have seen the gate 2023 paper but you are not aware of the solution. Where you will get that? Don’t worry , Dr. Shilpa Mam had explained in detail all the solution of questions which appeared in the GATE EE 2023 of the subject Network Theory.

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In this article , we will provide a well-acquainted solution of** GATE EE 2023** Questions for the challenging subject Network Theory.

## GATE EE 2023 Networks Question

**Q.1. For the circuit shown, The instantaneous value of the Thevenin’s equivalent voltage (in Volts) across the terminals a-b at time t = 5 ms is _______ (Round off to 2 decimal places).**

**Solution :- **

**Step-1 :- **Let us solve this by source transformation, consider maximum value i= sin 1000t

i=1 A

Converting the current source into voltage source , the circuit will be

We get,

V_{th} = i_{x}(10-j10)

**Step-2 :-** Applying KVL in the loop,

10+j10-(10+j10)i_{x} +4i_{x }= 0 —(i)

i_{x}=\frac{10+j10}{16}

Putting value of i_{x }in eq. (i)

V_{th}=\left ( \frac{10+j10}{16} \right )(10-j10)

**V _{th} = 12.5 volts **

V_{th} = 12.5 Volts (Maximum Value)

V_{th} = 12.5 sin 1000 t (Final expression)

The instantaneous value of the Thevenin’s equivalent voltage (in Volts) across the terminals a-b at time t = 5 ms is _______ (Round off to 2 decimal places) is calculated as

V_{th} = 12.5 sin 1000t

= 12.5 sin 1000 x 5 x 10^{-3}

**V _{th }= -11.98 V**

The correct answer is -11.98 V.

So, simply for solving the Thevenin’s problem, you have to convert the circuit into equivalent circuit and then you can apply source transformation, KVL to solve it further.

Hope, so. You have well understood the solution of the problem.

## Best Course for Networks

By Dr. Shilpa Sambhi