Physics

Problem

An inductor of

L = 150\,\text{mH}

is connected in series with a capacitor of

C = 0.05\,\mu\text{F}

. The resistance of the circuit can be neglected. (a) Determine the numerical value and sign of

(X_L - X_C)

at a frequency of

1.0\,\text{kHz}

. (b) Hence find the magnitude of the impedance at this frequency.

Intuitive explanation

In an LC circuit, the inductor and capacitor have opposite effects on current flow—one resists changes by storing energy in a magnetic field, the other by storing it electrically. The key is calculating their individual reactances $X_L = 2\pi f L$ and $X_C = 1/(2\pi f C)$ , then finding their net opposition. The sign of $(X_L - X_C)$ tells you whether the circuit behaves inductively or capacitively at that frequency, and since resistance is zero, the total impedance is simply the magnitude of this difference.

Intuitive explanation

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