Find Currents I1 and I2 in an Electric Circuit

[Harshna]

Homework Statement

I need to find the currents I1 and I2 in the attached image, but am having some difficulties grasping the concepts. I am given E(t) = 338sin(t) as well as values for R, L and C. I think I know what I need to use but I am not sure how to put it all together

Homework Equations

Kirchhoff’s Voltage Law
Kirchhoff's Current Law
I1 = L d²I/dt² + R dI/dt + I/c = E(t)
I2 = R dI/dt + I/C

The Attempt at a Solution

I have tried a bunch of things but I don't think any of them are right

 

[cnh1995]

What are the values of R, L and C?

I1 = L d2I/dt2 + R dI/dt + I/c = E(t)
I2 = R dI/dt + I/C

These equations are incorrect.
But, you don't have use DEs unless you want a complete time-domain solution (transient+steady state). You only need steady state currents here, so use phasor algebra.

I have tried a bunch of things but I don't think any of them are right

You need to show what you've tried.

 

[Harshna]

Hi cnh1995,

R = 5 Ohms, L = 1 Henry, C = 0.02 Farad

Thanks - unfortunately Lecturer said that we have to use differential equations.

I have tried solving with differential equations to find I(t) - but this doesn't really find the answer

 

[cnh1995]

Which course is this assignment from? If it is from ac circuits course, I am sure you don't need DEs at all.

Hi cnh1995,

R = 5 Ohms, L = 1 Henry, C = 0.02 Farad

Thanks - unfortunately Lecturer said that we have to use differential equations.

I have tried solving with differential equations to find I(t) - but this doesn't really find the answer

You'll have second order DEs with two variables. It would get very complicated.
The phasor approach will take less than five steps to find the (steady state) currents.