Question

A 2.0 mH inductor is connected in parallel with a variable capacitor. The capacitor can be varied from 100 pF to 200 pF. What is the range of oscillation frequencies for this circuit?

Short answer

The range of oscillation frequencies is 3.53 Hz - 5.03 Hz.

Step-by-step solution

Given information 

We have given that, a 2.0 mH inductor is connected in parallel with a variable capacitor. The capacitor can be varied from 100 pF to 200 pF.

.

The formula to calculate the oscillation frequency is :$f=\frac{1}{2\pi \sqrt{LC}}$

Here, $f$= Oscillation frequency

$L$= Inductance

$C$= Capacitance

As the capacitance vary between two values, we will calculate oscillation frequency for both values separately.

Step 2. 

Calculating value for $C=100\times {10}^{-15}$

localid="1651033231481" $f_1=\frac{1}{2\pi \sqrt{(2\times {10}^{-3}H)(100\times {10}^{-12}F)}}$

$f_1=3.55MHz$

Now we will calculate for $C=200\times {10}^{-15}$

localid="1651033320655" $f_2=\frac{1}{2\pi \sqrt{(2\times {10}^{-3}H)(200\times {10}^{-12}F)}}$

$f_2=5.03MHz$

So the range of oscillation frequency is 3.53 MHz - 5.03 MHz.