An inductor has a current I(t)= (0.500 A)cos[(275 )t] flowing through it.If the maximum emf across the inductor is equal to 0.500 V,what is the self-inductance of the inductor?
A) 4.37 mH
B) 3.64 mH
C) 2.75 mH
D) 0.73 mH
E) 1.43 Mh

Question

An inductor has a current I(t)= (0.500 A)cos[(275  )t] flowing through it.If the maximum emf across the inductor is equal to 0.500 V,what is the self-inductance of the inductor?
A) 4.37 mH 
B) 3.64 mH 
C) 2.75 mH 
D) 0.73 mH 
E) 1.43 Mh

Quizplus · Accepted Answer

The maximum emf across an inductor is given by:
$V_{max}=L\frac{di}{dt}$

Here, $V_{max}=0.500	ext{ V}$ and $i(t)=0.500\cos(275t)$

Taking the derivative of $i(t)$, we get:
$\frac{di}{dt}=-0.500(275)\sin(275t)$

Therefore, substituting the given values in the above equation, we get:
$L=\frac{V_{max}}{\frac{di}{dt}}=\frac{0.500}{-0.500(275)\sin(275t)}$

Taking the time to be $t=0$, we get:
$L=\frac{0.500}{-0.500(275)\sin(0)}=3.64	ext{ mH}$

Therefore, the self-inductance of the inductor is 3.64 mH, which is given by answer B.

An Inductor Has a Current I(t)= (0