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.