Question

A coil having a resistance and inductance of 5-ohm and 32 mH respectively is connected in series with 796pF capacitor. Determine the resonant frequency of the circuit.​

Answer 1

Given:

A coil having a resistance and inductance of 5-ohm and 32 mH respectively is connected in series with 796pF capacitor.

To find:

Resonant frequency of the circuit.

Calculation:

Let resonant frequency be f ;

General expression for "f" in an L-C circuit is:

$\boxed{ \sf{f = \dfrac{1}{2\pi \sqrt{LC} } }}$

Putting the available values in SI unit:

$= > \sf{f = \dfrac{1}{2\pi \sqrt{(32 \times {10}^{ - 3} ) \times (796 \times {10}^{ - 12} )} } }$

$= > \sf{f = \dfrac{1}{2\pi \sqrt{(32 \times796 \times {10}^{ - 15} )} } }$

$= > \sf{f = \dfrac{1}{2\pi \sqrt{(25472 \times {10}^{ - 15} )} } }$

$= > \sf{f = \dfrac{1}{2\pi \sqrt{(25.47 \times {10}^{ - 12} )} } }$

$= > \sf{f = \dfrac{1}{2\pi (5.04 \times {10}^{ - 6}) }}$

$= > \sf{f = \dfrac{ {10}^{6} }{2\pi \times 5.04 }}$

$= > \sf{f = \dfrac{ {10}^{6} }{10.08\pi }}$

$= > \sf{f \approx \dfrac{ {10}^{6} }{10\pi }}$

$= > \sf{f \approx \dfrac{ {10}^{5} }{\pi } \: hz}$

So, final answer is:

$\boxed{ \red{ \bf{f \approx \dfrac{ {10}^{5} }{\pi } \: hz}}}$