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RESONANCE
Resonance is defined as the condition in a circuit containing at least one inductor and one capacitor, when the supply voltage and the supply current are in phase. Thus at resonance the equivalent impedance of the circuit is purely resistive. Since the supply voltage and the supply current are in phase, the power factor of a resonant circuit is unity.
TYPES OF RESONANT CIRCUITS
There are two types of resonant circuit – series resonant circuit and parallel resonant circuit.
• SERIES RESONANT CIRCUIT
Consider the simple case of a coil L and a capacitor C connected in series as in figure.
Since L and C are in series, the same current will flow through L and C. The two voltages VL and VC will oppose each other. If the values of L and C are chosen such that inductive reactance XL is equal to the capacitive reactance XC at the given frequency, the value of impedance (XL – XC) will be theoretically zero and a very high current will flow through the circuit. The circuit is then said to be resonant at this frequency. However in actual practice a coil will always have some resistance and the current flowing at resonance will be limited by the value of resistance R.
LCR RESONANT CIRCUITS
As mentioned earlier, a pure inductance is not obtainable in practice. Any coil will have some resistance depending up on the size of the wire used. Even the capacitance and connecting leads in an LC circuit will have resistance. So any resonant LC circuit is actually an LCR resonant circuit in which the resistance R plays an important part.
In a series RLC circuit, the resonance may be produced by varying the frequency. Keeping L and C constant; otherwise resonance may be produced by varying either L or C for a fixed frequency.
Consider a series RLC circuit as shown in figure.
The total impedance of the series circuit is,
Z = R + j (XL –XC) = R + j (L – (1/C)) (1)
Let XL = XC at a frequency fr Hz, then the impedance of the network is purely resistive therefore resonance can be defined as the condition which exists when the impedance of the network is purely resistive.
In the circuit shown, if R = 120 Vs is 240V, 50 Hz and XL and XC each equal to 316, the circuit will be resonant at this frequency.
Then, Z = = 120 
Actually the resistance 120 may be the sum of the resistance of the coil and the resistance placed externally in the circuit. These resistances are generally lumped together and shown as one resistance R for calculation purpose.
Current,
Voltage across the coil, VL = I x XL = 2 x 316 = 632V
Voltage across the capacitor, VC = I x XC = 2 x 316 = 632V
These two voltages are equal but opposite as shown in figure 3.2b
Note that the voltage developed across the coil VL and the voltage developed across the capacitor VC are several times greater than the applied voltage Vs. This phenomenon is called resonant voltage step up.