Question

What is an expression for the transform current through resistor R ?(see attachment)

Answer 1

Is the source voltage an arbitrary function of time?

Answer 2

The current flows from the source through the first inductor, and then it branches off; part of the current flows through a purely capacitive branch. and the rest of it flows into the other inductor, which is in series with a resistor. At any instant, the voltages across the branches are the same. We can use this information and Kirchoff's laws to set up a system of equations to determine the currents throughout the circuit, including the current through the resistor.

Answer 3

I will be doing some pencil-and-paper calculations on this, so it may be some time before my next post here.

Answer 4

Tank you for your time !!!!!!!

Answer 5

I get\[L^{2}Ci'''_R + RLCi''_R + Li'_R = e(t)\]for the time-domain equation.
Since we are taking Laplace transforms of derivatives up to third-order,
\[i''_R(0), i'_R(0),\]and\[i_R(0)\]enter into my calculations. Since nothing
is stated about initial values for the current across the resistor, I keep those
three numbers arbitrary, leaving them in symbolic form. When I take the
Laplace transform of both sides of the equation I came up with,
I get
\[I_R(s) = E(s)/(L^{2}Cs^{3}+ RLCs^{2} + Ls)\]
\[+ L^{2}Ci_R(0)s^{2}/(L^{2}Cs^{3} + RLCs^{2}+ Ls)\]
\[+ (L^{2}Ci'_R(0) + RLCi_R(0))s/(L^{2}Cs^{3} + RLCs^{2} + Ls)\]
\[+ (L^{2}Ci''_R(0) + RLCi'_R(0) + LI_R(0))/(L^{2}Cs^{3} + RLCs^{2} + Ls).\]I get\[L^{2}Ci'''_R + RLCi''_R + Li'_R = e(t)\]for the time-domain equation.
Since we are taking Laplace transforms of derivatives up to third-order,
\[i''_R(0), i'_R(0),\]and\[i_R(0)\]enter into my calculations. Since nothing
is stated about initial values for the current across the resistor, I keep those
three numbers arbitrary, leaving them in symbolic form. When I take the
Laplace transform of both sides of the equation I came up with,
I get
\[I_R(s) = E(s)/(L^{2}Cs^{3}+ RLCs^{2} + Ls)\]
\[+ L^{2}Ci_R(0)s^{2}/(L^{2}Cs^{3} + RLCs^{2}+ Ls)\]
\[+ (L^{2}Ci'_R(0) + RLCi_R(0))s/(L^{2}Cs^{3} + RLCs^{2} + Ls)\]
\[+ (L^{2}Ci''_R(0) + RLCi'_R(0) + LI_R(0))/(L^{2}Cs^{3} + RLCs^{2} + Ls).\]

Answer 6

Thank you !!!!!!!!

Answer 7

You're welcome :^)