Answer:
The value of the inductance is 175.9 mH.
Explanation:
Given that,
Capacitor [tex]C= 40.0\ \muF[/tex]
Frequency = 60.0 Hz
The inductor and capacitor is connected in parallel, the voltage across each of these elements is the same.
We have,
[tex]V_{L}=V_{C}[/tex]
Using ohm's law
[tex]I_{rms}\times X_{L}=I_{rms}\times X_{C}[/tex]
[tex]X_{L}=X_{C}[/tex]
[tex]2\pi f L=\dfrac{1}{2\pi f C}[/tex]
[tex]L=\dfrac{1}{4\pi^2\times f^2\times C}[/tex]
Put the value into the formula
[tex]L=\dfrac{1}{4\times\pi^2\times60.0^2\times40\times10^{-6}}[/tex]
[tex]L=0.1759\ H[/tex]
[tex]L=175.9\times10^{-3}\ H[/tex]
[tex]L=175.9\ mH[/tex]
Hence, The value of the inductance is 175.9 mH.
