Question

Consider the following statements:

If a high Q parallel resonant circuit is loaded with a resistance

1. The circuit admittance reduces.

2. The resonant frequency remains the same.

3. The bandwidth reduces.

Which of the above statements is/are correct?

1. 3 only
2. 2 only
3. 1 only
4. 1, 2 and 3

Answer 1

Correct Answer - Option 2 : 2 only

Concept:

In a parallel RLC circuit, at resonant condition

The resonant frequency \({\omega _0} = \frac{1}{{\sqrt {LC} }}\)

Quality factor \(Q = R\sqrt {\frac{C}{L}} = {\omega _0}RC\)

Bandwidth \(= \frac{{{\omega _0}}}{Q} =\frac 1{RC}\)

Impedance = R

Application:

If the circuit is loaded with a resistance i.e. some resistance is added in parallel, the effective resistance in the circuit decreases. It affects the different parameters as explained below.

• The circuit impedance reduces as the new resistance is added in parallel.
• The resonant frequency remains the same as it is independent of the resistance (R).
• The bandwidth increases as effective resistance decreases.