Given:
[tex]X_{L} = 50.0 \ohm[/tex]
frequency, f = 60.0 Hz
frequency, f' = 45.0 Hz
[tex]V_rms} = 85.0 V[/tex]
Solution:
To calculate max current in inductor, [tex]I_{L(max)[/tex]:
At f = 60.0 Hz
[tex]X_{L} = 2\pi fL[/tex]
[tex]50.0 = 2\pi\times 60.0\times L[/tex]
L = 0.1326 H
Now, reactance [tex]X_{L}[/tex] at f' = 45.0 Hz:
[tex]X'_{L} = 2\pi f'L[/tex]
[tex]X'_{L} = 2\pi\times 45.0\times 0.13263 = 37.5\ohm [/tex]
Now, [tex]I_{L(max)[/tex] is given by:
[tex]I_{L(max) = \sqrt {\frac{2V_{rms}}{X'_{L}}}[/tex]
[tex]I_{L(max) = \sqrt {\frac{2\times 85.0}{37.5}} = 2.13 A[/tex]
Therefore, max current in the inductor, [tex]I_{L(max)[/tex] = 2.13 A
