The input from the DC source V, is a unit step function scaled by the magnitude of V. The forcing function for the differential equation is:View attachment 280068
I want to understand how do you approach this question after forming the KVL equation and differentiating. We were given the values for R = 1.5 Ohms, L = 0.9 H, C = 9 mF and V = 69V. I just want to know how do we go about it?
Thank YouThe input from the DC source V, is a unit step function scaled by the magnitude of V. The forcing function for the differential equation is:
\( V(t)\;=\;V_{dc}u(t) \)
where u(t) is 0 for t<0 and 1 for t≥1
That's a pathological case.asymptotically the limiting value of Vdc without ever actually reaching it.
Thank YouFrom Kirchhoff`s law we know that the sum of all voltages across the 3 componenets is identical to V.
Therefore:
i*R + L*d(i)/dt + (1/C)*Int(i*dt)=V.
After multiplying with C and differentiating again (d/dt), you arrive at the classical 2nd-order differential equation.
Such an equation can be solved with i(t)=Io*exp(st).
As the last step, solve for d(i)/dt for t=0.
It is true that there is mathematics and there is engineering. Both viewpoints are worth understanding.That's a pathological case.
In reality, when the voltage reaches to within the thermal voltage noise value of the circuit it has practically reached the input voltage value.
by Jake Hertz
by Jake Hertz
by Aaron Carman