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When a DC voltage is applied to an inductor, the current through it is found to build up in accordance with I = 20(1-e^-50t). After the lapse of 0.02 s, the voltage is equal to 2 V. What is the value of inductance?(a) 2 mH(b) 5.43 mH(c) 1.54 mH(d) 0.74 mHI had been asked this question by my school principal while I was bunking the class.Asked question is from Problems Involving Dot Conventions in chapter Resonance & Magnetically Coupled Circuit of Network Theory

Answer»

Right CHOICE is (b) 5.43 mH

The best EXPLANATION: VL = L\(\frac{dI}{dt}\)

Where, I = 20(1-e^-50t)

Therefore, VL = L\(\frac{d 20(1-e^{-50t})}{dt}\)

= L × 20 × 50e^-50t

At t = 0.02 s, VL = 2 V

∴ L = \(\frac{2}{20 × 50 × e^{-50×0.02}}\)

= 5.43 μH.



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