Final answer:
To find the equation for the current in an RLC circuit with given values of resistors, inductors, capacitors, and applied voltage, you need to determine the total impedance of the circuit and use Ohm's law. The impedance is calculated using the resistance, inductive reactance, and capacitive reactance.
Step-by-step explanation:
An RLC circuit is a type of electrical circuit that contains resistors (R), inductors (L), and capacitors (C).
The equation for the current, i(t), in this circuit can be determined using Kirchhoff's laws. In this case, the applied voltage to the circuit is given by E(t) = 20e^(-4t) + 5cos(t), where t represents time.
To find the current, we need to determine the total impedance of the circuit, which is the total opposition to the flow of current.
The impedance is given by Z = R + j(Xl - Xc), where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance.
The inductive reactance Xl and the capacitive reactance Xc can be calculated as Xl = 2πfL and Xc = 1/(2πfC), where f is the frequency of the applied voltage, L is the inductance, and C is the capacitance.
Once we have the impedance, we can use Ohm's law, V = IZ, where V is the voltage across the circuit and I is the current, to find the equation for the current in the RLC circuit.