Consider the following statements with respect to a parallel R-L-C circuit:

1. The bandwidth of the circuit decreases if R is increased.

2. The bandwidth of the circuit remains the same if L is increased.

3. At resonance, the input impedance is a real quantity.

4. At resonance, the magnitude of the input impedance attains its minimum value.

Which of the above statements are correct?

Parallel RLC circuit:

The characteristic equation is given as,

\({s^2} + \frac{1}{{RC}}s + \frac{1}{{LC}} = 0\)

The bandwidth of a parallel RLC network is given as:

\({\rm{BW}} = \frac{{{{\rm{\omega}}_{\rm{r}}}}}{{\rm{Q}}}=\frac{1}{RC}\)

Observations:

• The bandwidth is inversely proportional to the resistance, i.e. as the resistance increases, the bandwidth decreases.
• The bandwidth is independent of inductance. Hence the bandwidth of the circuit remains the same if L is increased.
• At resonance, the imaginary part of the net impedance becomes zero, which makes the input impedance a real quantity.
• Also, at resonance, the input impedance for a parallel resonant circuit attains a maximum value. This is opposite to a series resonance where at resonance, the impedance attains a minimum value.