The Series RLC Circuit — Question 9

Question 9

A leading current determines the capacitance only after its sign is used

A series circuit has R=30.0 ohms and L=.0500 H. At $\omega=1000$ radians per second its current leads the source voltage by 30 degrees.

1. Find C from the measured phase.

2. Find impedance magnitude and the resonance frequency relative to the measurement frequency.

Question 9 - Solution

A leading current determines the capacitance only after its sign is used

(a) Method and calculation

$$\tan\phi=(\omega L-1/(\omega C))/R,\quad\phi=-30^\circ.$$$$\boxed{C=\frac1{\omega(\omega L+R\tan30^\circ)}=14.8543\,\mu F}.$$

(b) Interpretation and further calculation

$$\boxed{Z=R/\cos30^\circ=34.6410\,\Omega}.$$$$\omega_0=1/\sqrt{LC}\Rightarrow\boxed{\omega_0=1160.35\,s^{-1}>1000\,s^{-1}}.$$

Physical check

A leading current means negative net reactance and operation below series resonance.