Laplace Transform (Problem 3) | Frequency Domain Analysis by using Laplace Transform in EXTC

TL;DR

This video explains how to solve a Laplace transform problem to find the current in a super mesh circuit.

Transcript

click the bell icon to get latest videos from ekeeda hello guys welcome to ekeeda welcome to this video on laplace transform problems let us see what problem number three is here you can see i have drawn a diagram and we are supposed to find i of t i of t is the current which is in the last loop there is a dependent voltage source whose value is 3 ... Read More

Key Insights

• 🦸 The problem involves solving a super mesh circuit with a dependent voltage source and a capacitor.
• 🔁 The initial circuit is solved at t=0- to find the currents in each loop.
• ⚡ The voltage across the capacitor is found using KVL, and it is determined to be -23 volts.
• 😃 The circuit at t>0 is solved using Laplace transforms to find the current, which is -1.667e^(-35t).
• 👻 Super mesh circuits allow additional equations to be written to solve for unknown currents.
• ❓ The value of the capacitor in the circuit is given as 3 farads.
• 🔨 Laplace transforms are a useful tool for analyzing circuits in the frequency domain.

Questions & Answers

Q: What does the term "super mesh" mean in the context of this circuit problem?

In this circuit, a super mesh is formed because there is a current source between two loops. It allows us to write additional equations to solve for the unknown currents.

Q: How is the voltage across the capacitor at t=0- calculated?

The voltage across the capacitor is calculated by applying KVL to the loop containing the capacitor, with all currents set to 0. The resulting equation is rearranged to isolate the voltage term, which is found to be -23 volts.

Q: How is the circuit at t>0 different from the initial circuit at t=0-?

At t>0, the switch in the circuit is in position 2, so the initial circuit containing the capacitor is replaced with an equivalent circuit consisting of the same capacitance and a voltage source of -23 volts.

Q: What is the Laplace transform of the equation obtained for the circuit at t>0?

The Laplace transform of the equation is obtained by applying the respective transforms to each term. This results in a transformed equation involving the Laplace transform of the current.

Summary & Key Takeaways

• The video discusses a problem involving finding the current in a super mesh circuit with a dependent voltage source and a capacitor.

• The initial circuit is solved at t=0- to find the values of the currents in each loop.

• The voltage across the capacitor is determined using KVL, and it is found to be -23 volts.

• The circuit at t>0 is then solved using Laplace transforms to find the current, which is found to be -1.667e^(-35t).