Question

The output voltage of an AC generator is given by Δv = (180 V) sin (70πt). The generator is connected across a 13.0-Ω resistor.
(a) By inspection, what is the maximum voltage?
V

(b) By inspection, what is the frequency?
Hz

(c) Find the rms voltage across the resistor.
V

(d) Find the rms current in the resistor.
A

(e) Find the maximum current in the resistor.
A

(f) Find the power delivered to the resistor.
W

(g) Find the current when t = 0.0050 s.
A

Answer 1

U = 180•sin (70πt).
Umax = 180 V
f=ω/2π=70π/2π =35 Hz,
rms U=Umax/√2= =0.707•Umax=0.707•180=127.3 V
U/R = (180/R)•sin (70πt)
I=(180/13) •sin (70πt)=13.85•sin (70πt)
Imax =13.85 A
rmsI= Imax/√2=0.707•Imax=
=0.707•13.85=9.8 A
Pmax=Imax•Umax=180•13.85=2493 W
P=I•U= 127.3•9.8 =1244.6W

I=13.85•sin (70πt)=
=13.85•si(70π •0.005)=
=13.85•0.89 =12.34 A