(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the current in them in this circuit, if we know [itex]R=X_L, X_C[/itex] and [itex]u=5sin(314t)[/itex]

3. The attempt at a solution

First , [itex]5=U_0, 314=\omega[/itex] and voltage we can write as [itex]u=U_0cos(\omega t + \frac{\pi}{2})[/itex] and [itex]u=U_0 e^{i\frac{\pi}{2}}=iU_0[/itex]. [itex]U[/itex] is the voltage at the source [itex]U_1[/itex] in the branch and [itex]U_2[/itex] at the resistor. Now [itex]U=U_1+U_2[/itex] or [itex]U=IR+IZ[/itex] where [itex]\frac{1}{Z}=\frac{1}{iL\omega}-\frac{C\omega}{i}[/itex] or [itex]Z=\frac{iL\omega}{1-CL\omega^2}[/itex]

Now the current is [itex]I=\frac{U}{R+Z}[/itex] or when it is arranged [itex]I=\frac{iU_0(1-CL\omega^2)}{iL\omega (2-CL\omega^2)}[/itex]. Now I don't know how to complete the calculation to reduce it to the form like this [itex]I_0sin(\omega t + \theta)[/itex].

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Solving circuit using complex numbers

**Physics Forums | Science Articles, Homework Help, Discussion**