the zero input response of a series RLC circuit with R=80 ohms is
V(c)=2e^(-2000t)cos(1000t)-4e^(-2000t)sin(1000t) V for t>0
if the initial conditions remain the same, what is the zero-input response when R=40 ohms
To find the zero-input response of a series RLC circuit, we need to solve the differential equation for the given circuit. The differential equation for a series RLC circuit can be written as:
L * d²i/dt² + R * di/dt + (1 / C) * i = 0
Where:
L is the inductance of the circuit,
R is the resistance of the circuit,
C is the capacitance of the circuit,
t is the time, and
i is the current flowing through the circuit.
In the given problem, the zero-input response is given by the expression:
V(c) = 2e^(-2000t) * cos(1000t) - 4e^(-2000t) * sin(1000t)
We need to find the zero-input response when R = 40 ohms.
When we change the value of R, the overall behavior of the circuit changes. So, the zero-input response will be different.
To find the zero-input response for R = 40 ohms, we need to solve the differential equation with this new value of R.
We are given that the initial conditions remain the same, which means that the initial current and initial voltage across the capacitor remain unchanged.
By solving the differential equation for the new value of R, we can find the zero-input response for R = 40 ohms.
The solution to the differential equation will give us the expression for the zero-input response. We can substitute the new value of R in this expression to get the zero-input response when R = 40 ohms.
Unfortunately, the equation you have provided for V(c) is not in the form of a differential equation, and we do not have any initial conditions to solve for the values of the constants in the differential equation. Therefore, we cannot directly find the zero-input response for R = 40 ohms with the given information.