Question

a) Show that capacitor voltage \( v \) is described by the differential equation below: [3] \[ c \frac{d^{2} v}{d t^{2}}+\frac{1}{\mathrm{R}} \frac{d v}{d t}+\frac{1}{L} v=\frac{d i_{g}}{d t} \quad \frac{1}{4 / 3} \] b) If \( R=1 \Omega, L=\frac{4}{3} H, C=\frac{1}{4} F \), and \( i_{g}=4 e^{-2 t} A \), write down the characteristic equation of the natural response. [2] c) Determine the general form of the natural response and determine whether this is an overdamped, under-damped or critically-damped case. [5] [5] d) Determine the forced response of the circuit. [2] e) Write the general expression for the complete response \( v(t) \) for \( t>0 \). f) Determine the values of the constants obtained in (c) if \( v(0)=2 \mathrm{~V}^{\prime} \mathrm{dnd} \frac{\mathrm{dv}(\mathrm{0})}{\mathrm{dt}}=4 \mathrm{Vs}^{-1} \) hence write down the complete solution for \( v(t) \) for \( t>0 \) [3] \[ a \frac{d^{2} y}{d t^{2}}+B \frac{d y}{d t}+c y=f(t) \]

          a) Show that capacitor voltage \( v \) is described by the differential equation below:
[3]
\[
c \frac{d^{2} v}{d t^{2}}+\frac{1}{\mathrm{R}} \frac{d v}{d t}+\frac{1}{L} v=\frac{d i_{g}}{d t} \quad \frac{1}{4 / 3}
\]
b) If \( R=1 \Omega, L=\frac{4}{3} H, C=\frac{1}{4} F \), and \( i_{g}=4 e^{-2 t} A \), write down the characteristic equation of the natural response.
[2]
c) Determine the general form of the natural response and determine whether this is an overdamped, under-damped or critically-damped case.
[5]
[5]
d) Determine the forced response of the circuit.
[2]
e) Write the general expression for the complete response \( v(t) \) for \( t>0 \).
f) Determine the values of the constants obtained in (c) if \( v(0)=2 \mathrm{~V}^{\prime} \mathrm{dnd} \frac{\mathrm{dv}(\mathrm{0})}{\mathrm{dt}}=4 \mathrm{Vs}^{-1} \) hence write down the complete solution for \( v(t) \) for \( t>0 \)
[3]
\[
a \frac{d^{2} y}{d t^{2}}+B \frac{d y}{d t}+c y=f(t)
\]

a) Show that capacitor voltage v is described by the differential equation below:
[3]

c (d^2 v)/(d t^2)+(1)/(R)(d v)/(d t)+(1)/(L) v=(d ig)/(d t) (1)/(4 / 3)

b) If R=1 Ω, L=(4)/(3) H, C=(1)/(4) F, and ig=4 e^-2 t A, write down the characteristic equation of the natural response.
[2]
c) Determine the general form of the natural response and determine whether this is an overdamped, under-damped or critically-damped case.
[5]
[5]
d) Determine the forced response of the circuit.
[2]
e) Write the general expression for the complete response v(t) for t>0.
f) Determine the values of the constants obtained in (c) if v(0)=2 V^'dnd(dv(0))/(dt)=4 Vs^-1 hence write down the complete solution for v(t) for t>0
[3]

a (d^2 y)/(d t^2)+B (d y)/(d t)+c y=f(t)

Added by Raymond G.

Question

Please give Ace some feedback