Question

For a series RLC resonant circuit, the resonant frequency is given as $8MHz$ and the bandwidth is $7.2kHz$. If the value of effective resistance is $4.5\Omega$ then the capacitance C will be equal to

• A. $0.49pF$
• B. $3.98pF$
• C. $12.45pF$
• D. $31.84pF$

Answer 1

The correct option is B $3.98pF$

For series RLC circuit,
$f_0=\frac{1}{2\pi }\sqrt{\frac{1}{LC}}$ ...(i)
and
$f_2-f_1=$ Bandwidth, $BW=\frac{1}{2\pi }\times \frac{R}{L}$ ...(ii)
from equation (i) and (ii)
$\frac{BW}{f_0^2}=\frac{\frac{1}{2\pi }\times \frac{R}{L}}{\frac{1}{4{\pi }^2}\times \frac{1}{LC}}=2\pi RC$
$C=\frac{BW}{2\pi \times R\times f_0^2}=\frac{7.2\times {10}^3}{2\times \pi \times 4.5\times 8\times {10}^6\times 8\times {10}^6}=3.978pF$