INTRODUCTION:
Resonance is the name given to a phenomenon when an object
shows maximum response when it is subjected to a certain frequency known as
‘resonant frequency’ or ‘natural frequency’ of that object. Resonance can be
both mechanical and electrical. Mechanical resonance can be observed in any
vibrating body such as tuning fork. However resonance in electrical circuits is
observed in RLC circuits.
RESONANCE
IN RLC CIRCUITS:
The
resonant circuit is a combination of R, L, and C elements having
a frequency response characteristic similar to the one appearing in
given figure.
Resonance
curve
Note
in the figure that the response is a maximum for the frequency fr,
decreasing to the right and left of this frequency. In other words, for a
particular range of frequencies the response will be near or equal to
the maximum.
CONDITION
FOR RESONANCE:
The required condition for resonance is that circuit’s
capacitive reactance becomes equal to its inductive reactance.
XL=XC
TYPES OF
RESONANCE:
There are two types of resonance based on how inductor and
capacitor are connected in the circuit:
I.
Series
Resonance
II.
Parallel
Resonance
SERIES
RESONANCE:
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Resonance in series circuits occur when the total reactance of the circuit becomes zero i.e. inductive and capacitive reactance have equal value and they cancel each other as they have a phase difference of 180⁰.
MINIMUM IMPEDANCE:
Since circuit elements are in series total impedance is given
by:
This is the minimum impedance of resonant circuit.
Phasor relationship of total impedance is given by the phasor
diagram given below.
MAXIMUM CURRENT:
At resonant frequency RLC circuit shows maximum response of
current.
Using Ohm’s law:
This show that current is inversely proportional to the impedance
of the circuit. In the resonance state impedance is minimum so current would be
maximum.
RESONANT FREQUENCY:
The resonant frequency can be determined in terms of the
inductance and capacitance by examining the defining equation for resonance.
UNIT POWER FACTOR:
The average power to the resistor at resonance is equal to I2R,
and the reactive power to the capacitor and inductor are I2XC
and I2XL respectively. The power triangle shows that the
total apparent power of the circuit is equal to power dissipated due to
resistor.
Power triangle for series resonant circuit at
resonance
The power factor for circuit at
resonance is:
PARALLEL
RESONANCE:
Resonance in parallel circuits occurs when the parallel impedance is maximum. The current is in phase with the voltage during parallel resonance.
The circuit resonates at a frequency which makes the
inductive reactance XL and the capacitive reactance XC
equal, so the two branch currents i.e. through inductor and through capacitor
are equal but opposite in direction. Hence they cancel out the effect of each
other and as a result the net current drawn from the source is zero. In actual
practice the current is not exactly zero but has a minimum value due to small
resistance of the coil.
MAXIMUM IMPEDANCE:
Since circuit is in parallel its admittance is given by:
This shows that in parallel resonance circuits minimum
admittance is observed. So impedance is maximum.
MINIMUM CURRENT:
At resonant frequency parallel RLC circuit shows minimum
current.
Using Ohm’s law:
This show that current is inversely proportional to the impedance
of the circuit. In parallel circuits IMPEDANCE is maximum so current would be
minimum at resonance state.
RESONANT FREQUENCY:
In parallel circuits resonant
frequency is same as series circuits i.e.
EXPLANATION
OF RESONANCE PHENOMENON IN PARALLEL CIRCUITS:
At resonance, the branch currents IC
and IL each may be larger than the source current. The reason is
that the current impedance is high, the overall current is zero but the voltage
developed across the parallel circuit is high. The individual currents
developed in the inductance IL and capacitance IC at
resonance can be very large but are out of phase with each other resulting in very
low combined current.
UNIT POWER FACTOR:
The average power to the resistor at resonance is equal to I2R,
and the reactive power to the capacitor and inductor are I2XC
and I2XL respectively. The power triangle shows that the
total apparent power of the circuit is equal to power dissipated due to
resistor.
Power triangle for parallel resonant circuit at resonance
The power factor for circuit at resonance
is:
