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Chapter 30: Q. 69 (page 874)

69. II The current through inductance Lis given byI=I0sin蝇t .

CALC a. Find an expression for the potential difference螖VL across the inductor.

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

Short Answer

Expert verified

Part (a) The expression for potential difference across the inductor is螖VL=鈭�L蝇Iecos蝇t

Part (b) The maximum voltage across the inductor is 1.27脳10鈭�3A

Step by step solution

01

Part (a)

The current in the inductor at any instant of time is I=Iesin蝇t

Here, 蝇is 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=ddtIesin蝇t

=蝇I0cos蝇t

The potential difference across the inductance is

role="math" 螖VL=鈭�LdIdt鈭�L蝇Iocos蝇t

Therefore, the expression for potential difference across the inductor is

螖VL=鈭�L蝇Iecos蝇t

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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