The RLC circuit given in figure below can be solved A. Current i(t) can be solved using KVL B. Current i(t) can be solved using KCL C. Current i(t) can be solved using fourier transform D. Current i(t) can be solved using laplace transform E. Current i(t) can be solved using Fourier series Choose the correct answer from the options given below:
A & D only
The RLC circuit question involves determining the methods by which the current \( i(t) \) can be solved. Let's examine each of the given options:
- Using Kirchhoff's Voltage Law (KVL):
- KVL is applicable to this circuit. By applying KVL, the sum of the potential differences around the loop can be set equal to zero, thereby allowing us to write a differential equation involving the current \( i(t) \).
- This method will be effective, particularly because the circuit is linear and can be analyzed using classical methods.
- Using Kirchhoff's Current Law (KCL):
- KCL is generally used to analyze nodal points, not loops. In this single-loop circuit, KVL is more directly applicable than KCL.
- Hence, KCL is not suitable for solving for \( i(t) \) here.
- Using Fourier Transform:
- The Fourier Transform is used to analyze the frequency components of a signal, generally in steady-state AC analysis. It is less suitable for time-domain transient analysis directly applicable here.
- Using Laplace Transform:
- The Laplace Transform is a powerful tool for solving linear differential equations by transforming them into algebraic equations. It is highly applicable for analyzing RLC circuits as it simplifies circuit equations in the frequency domain.
- Thus, it can be used effectively to solve for \( i(t) \).
- Using Fourier Series:
- The Fourier Series is useful for periodic signals and doesn't directly solve time-dependent transient behavior in circuits like the RLC under analysis.
- Therefore, it is not suitable for solving \( i(t) \).
Based on the analysis, the correct methods to solve for the current \( i(t) \) are using KVL and Laplace Transform. Therefore, the correct answer is A & D only.
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