RLC Circuit (with variable frequency)

[meb09JW]

Homework Statement

Find the frequency at which the circuit becomes purely resistive and calculate the effective resistance.

Here is the circuit with the given solution-

The trouble is, whilst the solution is simple enough, there are many places to go wrong, and the whole process is time comsuming. I've managed to simplify a few other answers given in this answer booklet, but for this one, i can't find an easier method.

Any ideas? I can't find a similar example in Hughes.

Thanks,
Josh.

 

[ehild]

If Z is real so is 1/Z.

$$\frac{1}{Z}=\frac{R-j\omega L}{R^2+(\omega L)^2}+j\omega C=\frac{R}{R^2+(\omega L)^2}+j\omega( C-\frac{ L}{R^2+(\omega L)^2})$$

ehild