Question

A 20Ω resistance, 10 mH inductance coil and 15µF capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance is made \[\frac {1}{3}\] rd, the resonant frequency ______.

Options

• remains unchanged.

• is doubled.

• is quadrupled.

• is halved.

Answer 1

A 20Ω resistance, 10 mH inductance coil and 15µF capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance is made \[\frac {1}{3}\] rd, the resonant frequency remains unchanged.

Explanation:

At resonance, X_L = X_C

⇒ ωL = \[\frac {1}{ωC}\]

⇒ ω² = \[\frac {1}{\sqrt {LC}}\]

⇒ f = \[\frac {1}{2π\sqrt {LC}}\]   ...(i)

From (i), we can see that the resonant frequency is independent of R (resistance).

So, if the resistance is made (\[\frac {1}{3}\])^rd, the resonant frequency remain unchanged.