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Chapter 30: Q. 69 (page 874)

69. II The current through inductance Lis given byI=I0sinωt .

CALC a. Find an expression for the potential differenceΔVL across the inductor.

b. The maximum voltage across the inductor is 0.20Vwhen L=50μHand f=500kHz. What isI0 ?

Short Answer

Expert verified

Part (a) The expression for potential difference across the inductor isΔVL=−LωIecosωt

Part (b) The maximum voltage across the inductor is 1.27×10−3A

Step by step solution

01

Part (a)

The current in the inductor at any instant of time is I=Iesinωt

Here, ωis the angular frequency, tis the time taken by the current in the inductor, and Ieis the maximum current in the inductor.

Differentiate the equation with respect to time t.

dIdt=ddtIesinωt

=ωI0cosωt

The potential difference across the inductance is

role="math" ΔVL=−LdIdt−LωIocosωt

Therefore, the expression for potential difference across the inductor is

ΔVL=−LωIecosωt

02

Part (b)

Convert the units for inductance from to .

Convert the units for frequency from to

The maximum cosine value varies from +1 to -1 . So the maximum potential difference across the inductor is,

Rewrite the equation for current

Therefore, the maximum voltage across the inductor is

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