Worked examples

WORKED EXAMPLES

ON PARALLEL RESONANCE CIRCUITS

Example 1 For the parallel network shown in figure, determine the value of R for resonance.

Solution: The total admittance Y = Y₁ + Y₂

Example 2 A coil of 20 Ω resistance has an inductance of 0.2 H and is connected in parallel with a condenser of 100 uF capacitance. Calculate the frequency at which the circuit will act as a non-inductive resistance of R ohms. Find also the value of R.

Solution: The circuit is given to be acting as non-inductive resistance.

This means that the circuit is at resonance.

The resonant frequency is given by

fo = 1/2π × √1/LC – R¹₂ / L₂ … (i)

At resonance, Y = R₁ / R₁² + X_L²  ... (ii)

Substituting the values in equation (i), we get

Example 3 Find the values of R, and Rc for the circuit in the following fig in order that the circuit is to resonate at all frequencies. Derive the formula used.

Solution: For derivation, please refer parallel resonance case (c).

RL = RC = √L/C = √2.5 × 10^-3 / 50 × 10^-6

= 7.07 Ω

Example 4 Find resonant frequency of the circuit shown.

Solution:

Example 5 A current source is applied to a parallel combination of R, L and C, where R = 10 ohms, L = 1H and C =1 μF.

(a) Compute the resonant frequency.

(b) Find the quality factor.

(c) Calculate the value of the bandwidth.

(d) Compute the lower and upper half frequency points of the bandwidth.

Solution:

Example 6 Determine the value of the capacitance C in order that the circuit in the figure is resonant at 6366 Hz.

Solution:

At resonance, the reactie part of Y is equal to 0.