RLC Resonance

Question:

It is asked in my exercise to:
1. explain the term 'resonance' of a RLC circuit and
2. state and explain the 'conditions' for resonance of a RLC circuit
I know that resonance i a RLC circuit occurs when the angular frequency of the resistor, inductor and capacitor connected in parallel is equal to the angular frequency of the resistor, inductor and capacitor connected in series. But is this the definition of resonance or its condition?

Also, what do we mean by a 'low pass' filter in a RC circuit? I think when the frequency is high, Xc much less than R, most of the voltage will drop across R instead of across C. So a "low voltage" is measured if an electrometer is connected across the capacitor. However, instead of low voltage, it is said in the textbook that 'low frequencies are passed'. What does it mean? How can frequency be passed?

Answer:

Resonance is normally defined as the condition where the capacitive and inductive reactance are of equal magnitude. This condition leads to a resonance angular frequency equal to the reciprocal of the square root of the capacitance times the inductance. w=1/(LC)^.5. This is true for both series and parallel circuits, so your stated condition is true, even if not the normally used definition of resonance.

You are right regarding the low pass filter, the reactance of the capacitor is inversely proportional to to the frequency, so that higher frequency components of the signal appear across the resistor while lower frequencies appear across the capacitor. By taking the output from across the capacitor we see higher amplitude for the low frequency components of the signal.