Calculate the value of capacity in picofarad, which will make 101.4 microhenry inductance to oscillate with frequency of one megahertz.

Question

Calculate the value of capacity in picofarad, which will make 101.4 microhenry inductance to oscillate with frequency of one megahertz. (A) 250 pF (B) 249.6 pF (C) 240 pF (D) 242 pF

Tardigrade Admin · Accepted Answer

C =? L =101.4 μ H =101.4 × 10-6 H v=1 MHz =106 Hz As, v=(1/2 π √L C) ∴ C =(1/4 π2 v2 L) C =(1 × 7 × 7/4 × 22 × 22 × 1012 × 101.4 × 10-6) =2.496 × 10-10 farad C =249.6 pF

Q. Calculate the value of capacity in picofarad, which will make 101.4 microhenry inductance to oscillate with frequency of one megahertz.

$250 pF$

$249.6 pF$

$240 pF$

$242 pF$

$C = ? L = 101.4 μ H = 101.4 \times 1 0^{- 6} H$
$v = 1 M Hz = 1 0^{6} Hz$
As, $v = \frac{1}{2 π L C}$
$∴ C = \frac{1}{4 π ^{2} v ^{2} L}$
$C = \frac{1 \times 7 \times 7}{4 \times 22 \times 22 \times 1 0 ^{12} \times 101.4 \times 1 0 ^{- 6}}$
$= 2.496 \times 1 0^{- 10}$ farad
$C = 249.6 pF$

Q. Calculate the value of capacity in picofarad, which will make 101.4 microhenry inductance to oscillate with frequency of one megahertz.

250pF

249.6pF

240pF

242pF

C=?L=101.4μH=101.4×10−6H v=1MHz=106Hz As, v=2πLC​1​ ∴C=4π2v2L1​ C=4×22×22×1012×101.4×10−61×7×7​ =2.496×10−10 farad C=249.6pF

$250 pF$

$249.6 pF$

$240 pF$

$242 pF$

$C = ? L = 101.4 μ H = 101.4 \times 1 0^{- 6} H$
$v = 1 M Hz = 1 0^{6} Hz$
As, $v = \frac{1}{2 π L C}$
$∴ C = \frac{1}{4 π ^{2} v ^{2} L}$
$C = \frac{1 \times 7 \times 7}{4 \times 22 \times 22 \times 1 0 ^{12} \times 101.4 \times 1 0 ^{- 6}}$
$= 2.496 \times 1 0^{- 10}$ farad
$C = 249.6 pF$