Question

If the current through a 3 mH inductor is i(t)=80 cos150t mA , find the terminal voltage and the energy stored.

Answer 1

Terminal voltage, $V=-36\sin (150 t)\ mV$

Energy stored, $E=9.6\cos^2 (150 t)$

Explanation:

We have,

Inductance, L = 3 mH

Current through the inductor is given by :

$I(t)=80\cos (150t)\ mA$

(a)  The terminal voltage is given by :

$V=L\dfrac{dI}{dt}\\\\V=3\times 10^{-3}\times \dfrac{d(80\cos (150t)}{dt}\\\\V=-3\times 10^{-3}\times 80\sin (150 t) \times 150\\\\V=-36\sin (150 t)\ mV$

(b) Energy stored in the inductor is given by :

$E=\dfrac{1}{2}LI^2\\\\E=\dfrac{1}{2}\times 3\times 10^{-3}\times (80\cos (150 t))^2\\\\E=9.6\cos^2 (150 t)$

Hence, this is the required solution.

Learn more,

If the current through a 3 mH inductor is i(t)=80 cos150t mA , find the terminal voltage and the energy stored.

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