The output voltage of an AC generator is given by Δ v = (170 V) sin (60πt). The generator is connected across a 20.0-Ω resistor. By inspection, what are the (a) maximum voltage and (b) frequency? Find the (c) rms voltage across the resistor, (d) rms current in the resistor, (e) maximum current in the resistor, (f) power delivered to the resistor, and (g) current when t = 0.005 0 s. (h) Should the argument of the sine function be in degrees or radians?
The output voltage of an AC generator is given by Δ v = (170 V) sin (60πt). The generator is connected across a 20.0-Ω resistor. By inspection, what are the (a) maximum voltage and (b) frequency? Find the (c) rms voltage across the resistor, (d) rms current in the resistor, (e) maximum current in the resistor, (f) power delivered to the resistor, and (g) current when t = 0.005 0 s. (h) Should the argument of the sine function be in degrees or radians?
GIVEN:
Output voltage, Δv = (170 V) sin (60πt)
Resistance, R = 20.0-Ω
Part (a)
Standard equation can be represented as,
Δv = Vmsin(ωt)
Where, Vm = maximum voltage.
ω = angular frequency.
Compare the given equation with standard equation.
We get, Vm = 170 V Answer
Part (b)
Angular frequency, ω = 60π ... (1)
Also, ω = 2πf .... (2)
Equate both,
2πf = 60π
f = 60π/2π
f = 30 Hz Answer
Part (c)
RMS voltage is equal to 1/√2 times of maximum voltage.
Vrms = Vm/√2
Vrms = (170 V)/√2
Vrms = 120.208 V Answer
Part (e)
the maximum current through the resistor
Imax=I2Imax=(6.010)2Imax=8.499A
Part(f)
power delivered to the resistor
P=I2rmsRP=(8.499)2(20) P=722.4 W
Missing g and h
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