Answer:
The inductance and stored energy are 234 H and [tex]3.15\times10^{-4}\ J[/tex]
Explanation:
Given that,
Resistance R= 8.41 kΩ
Voltage V= 68.6 V
Current I = 1.64 mA
Time t = 6.26 ms
We need to calculate the maximum current of the coil
Using formula of maximum current
[tex]I_{max}=\dfrac{V}{R}[/tex]
[tex]I_{max}=\dfrac{68.6}{8.41\times10^{3}}[/tex]
[tex]I_{max}=8.15\times10^{-3}\ A[/tex]
We need to calculate the inductance of the coil
[tex]I_{f}=I(1-e^{\frac{-t}{\tau}})[/tex]
[tex]t=-\dfrac{L}{R}In(1-\dfrac{I_{f}}{I_{max}})[/tex]
[tex]6.26\times10^{-3}=-\dfrac{L}{8.41\times10^{3}}In(1-\dfrac{1.64\times10^{-3}}{8.15\times10^{-3}})[/tex]
[tex]L=\dfrac{{6.26\times10^{-3}\times8.41\times10^{3}}}{ln(1-\dfrac{1.64\times10^{-3}}{8.15\times10^{-3}})}[/tex]
[tex]L=234\ H[/tex]
(b). We need to calculate the stored energy
Using formula of stored energy
[tex]U=\dfrac{1}{2}LI^2[/tex]
[tex]U=\dfrac{1}{2}\times234\times(1.64\times10^{-3})^2[/tex]
[tex]U=3.15\times10^{-4}\ J[/tex]
Hence, The inductance and stored energy are 234 H and [tex]3.15\times10^{-4}\ J[/tex]
