Answer:
Inductance, L = 0.0215 Henry
Explanation:
Given that,
Capacitance of the capacitor, [tex]C=7.7\ nF=7.7\times 10^{-9}\ F[/tex]
Potential difference, V = 12 V
The period of oscillation, [tex]t=8.1\times 10^{-5}\ s[/tex]
At resonance, the angular velocity is given by :
[tex]\omega=\dfrac{1}{\sqrt{LC} }[/tex]
[tex]\dfrac{2\pi}{t}=\dfrac{1}{\sqrt{LC} }[/tex]
[tex]L=\dfrac{t^2}{4\pi^2C}[/tex]
[tex]L=\dfrac{(8.1\times 10^{-5})^2}{4\pi^2\times 7.7\times 10^{-9}}[/tex]
L = 0.0215 Henry
So, the inductance of the coil is 0.0215 Henry. Hence, this is the required solution.
