physics 102

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?

(b) By inspection, what is the frequency?

(c) Find the rms voltage across the resistor.

(d) Find the rms current in the resistor.

(e) Find the maximum current in the resistor.

(f) Find the power delivered to the resistor.

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

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  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

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