Physics: The current through an inductor of inductance L is given by I(t) = Imax sin(ωt). (a) Derive an expression for the induced emf in the inductor as a function of time. (b) At t = 0, is the current through the inductor increasing or decreasing? (c) At t = 0, is the induced emf opposing or aiding the flow of the charge carriers? (Remember that the direction of a positive induced emf is the same as the current direction and the direction of a negative induced emf is opposite the current direction.) (d)

It is launched with a speed of 11 m/s.Explanation:...

The current through an inductor of inductance L

versaceblooper

28.01.2022

(a) $emf_L=-LI_{max}\omega cos(\omega t)$

(b) neither increasing or decreasing

Explanation:

The current through an inductor of inductance L is given by:

$I(t)=I_{max}sin(\omega t)$ (1)

(a) The induced emf is given by the following formula

$emf_L=-L\frac{dI}{dt}$ (2)

You derivative the expression (1) in the expression (2):

$emf_L=-L\frac{d}{dt}(I_{max}sin(\omega t))\\\\emf_L=-LI_{max}\omega cos(\omega t)$

(b) At t=0 the current is zero

$emf_L=-\omega LI_{max}$

w, L and Imax have positive values, then the emf is negative. Hence, the induced emf is opposite to the flow of the charge carriers.

(d) read the text carefully

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