I need help with (f), (g) and (h) please. The output voltage of an AC generator

Question

I need help with (f), (g) and (h) please.

The output voltage of an AC generator is given by v = (1.10 102 V)sin(42t). The generator is connected across a 0.500 H inductor. Find the following.

(a) frequency of the generator
21 Hz

(b) rms voltage across the inductor
77.8 V

(c) inductive reactance
66

(d) rms current in the inductor
1.178 A

(e) maximum current in the inductor
1.67 A

(f) average power delivered to the inductor
_____ W

(g) Find an expression for the instantaneous current. (Use the following as necessary: t.)
i= ______

(h) At what time after

t = 0

does the instantaneous current first reach 1.00 A? (Use the inverse sine function.)
______ ms

Explanation / Answer

average power=irms*vrms*cos(phi)

in the inductor circuit phi =90

so average power=0

i=i0*sin(wt-pi/2)

i=1.67*sin(42*pi*t-pi/2)

if i= 1A

cos(42*pi*t)=1/1.67

t=7.03 ms

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