Type 22 (Combination of Resistance and Capacitor-Inductor in Steady State) | Transient Analysis

TL;DR

This content explains the steps to derive the equation for the current in a circuit with a given voltage function.

Transcript

so let's have a few more examples uh in this circuit if you observe carefully the value of voltage is given as 4 into e raised to minus 3t and again i need to find the equation for i of t so let's first put the value for v of t so the equation will be 4 e raised to minus 3t let's switch 0.5 ohms having the inductor 0.25 so i need to find i of t so ... Read More

Key Insights

• ❓ The circuit conditions at t=0-, t=0+, and t>0+ determine the behavior of the current.
• 👮 KVL and Ohm's law are applied to derive the differential equation for the current.
• 💁 The differential equation is then simplified by dividing throughout by the coefficient to obtain the standard form.
• 😝 The final equation for the current is found by substituting the values of 'p', 'q', and 'k' into the standard form.
• 🍉 The equation for the current includes exponential terms that depend on the values of the voltage function and the inductor.
• 🌆 The constant 'k' in the current equation is determined by setting the value of the current at t=0 equal to the initial current value.
• ⌛ By solving the current equation, you can determine the values of the current at different times in the circuit.

Questions & Answers

Q: How do you find the current in a circuit for different time conditions?

To find the current, you need to consider the circuit conditions at t=0-, t=0+, and t>0+. By applying Kirchhoff's voltage law and Ohm's law, you can derive the differential equation for the current and then simplify it to find the final equation.

Q: What happens to the circuit at t=0- and t=0+?

At t=0-, the circuit is open, so the current value is zero. At t=0+, the circuit is closed, but the initial current is still zero because the inductor opposes the current flow.

Q: What is the equation for the current in the circuit for t>0+?

For t>0+, the equation for the current is given as i(t)=0.94[e^(-3t) - e^(-20t)].

Q: How do you find the constant value 'k' in the current equation?

To find 'k', you need to put the value of t=0 in the current equation and set it equal to the initial current value, which is 0. Solving for 'k' gives you the value.

Summary & Key Takeaways

• The content discusses the process of finding the equation for the current in an electric circuit, given the voltage function.

• It explains the three different conditions for the circuit: at t=0-, at t=0+, and for t>0+.

• The content applies Kirchhoff's voltage law (KVL) and Ohm's law to derive the differential equation for the current, which is then simplified to find the final equation.