Question

A 10-mh inductor has a parasitic series resistance of rs = 0.5 ω, as shown below. If the current is given by i(t) = 0.1 sin(20t) a, find vr(t) , vl(l), and v(t).

Answer 1

`v_r(t)=r\cdot i(t)=(0.5\,\Omega)(0.1sin((20t)\,A))=0.05sin((20t))\,V\\\\v_l(t)=l\cdot (d)/(dt)(i(t))=(0.010\,H)(20\cdot 0.1cos((20t)\,A/s))=0.02cos((20t)\,V)`

Then the total voltage is ...

`v(t)=(0.05sin((20t))+0.02cos((20t)))\,V\approx 0.05385sin((20t+0.3805)\,V)`

The magnitude of the resultant voltage is √(.02²+.05²); the angle is arctan(.02/.05).