Question

12. An LC circuit oscillates at a frequency of$2000\text{Hz}$ . What will the frequency be if the inductance is quadrupled?

Short answer

If the inductance is quadrupled, the value of the frequency will be $1000\text{Hz}$

Step-by-step solution

Step 1. Given information

Initial frequency:$f=2000\text{Hz}$

The frequency of a LC circuit is given by

$f=\frac{1}{2\pi \sqrt{LC}}$

Step 2. Explanation

Consider the inductance and capacitance of the circuit is L and C, hence the initial frequency of the circuit is

$f_i=\frac{1}{2\pi \sqrt{LC}}$

If the inductance is quadrupled, the new inductance of the inductor will be 4L, hence, the final frequency of the circuit will be

$f_f=\frac{1}{2\pi \sqrt{4LC}}=\frac{1}{2}\frac{1}{2\pi \sqrt{LC}}=\frac{1}{2}(2000\text{Hz})=1000\text{Hz}$

If the inductance is quadrupled, the value of the frequency will be$1000\text{Hz}$