Question

A light bulb is connected to a 60-V wall socket. The current in the bulb depends on the time t according to the relation I = (1.414 A) sin[(282.6 Hz)t].

(a) What is the frequency of the alternating current? Hz

(b) Determine the resistance of the bulb's filament? Ω

(c) What is the average power delivered to the light bulb? W

Answer 1

the stantard expression of sinusoidal alternating current i= Im sin(t)  

=angular frequency(radian/sec) =282.6 =2f    /f=frequency(Hz)

frequency=/2 =282.6/2=45 hertz

in your expression of current mension 282.6Hz i think it is mistake mostly it may be radian/second because 282.6Hz power supply rare in use

Im =maximum current

t= instantaneos time

the frequency of the alternating current=

2)the resistance of the bulb's filament = Vm /Im

Vm and Im are the maximum voltage and maximum current

Vm=Vrms x =60x = 84.85volt

Im=1.414 A

so resistance of the bulb's filament = Vm /Im =84.85volt/1.414 A =60ohm

3)average power = Vm xIm/2 =84.85volt x1.414 A/2 =56watts