A light bulb is connected to a 120V wall socket The current

A light bulb is connected to a 120-V wall socket. The current in the bulb depends on the time t according to the relation I = (1.414 A) sin[(31.4 Hz)t]. (a) What is the frequency of the alternating current? Incorrect: Your answer is incorrect. . Hz (b) Determine the resistance of the bulb\'s filament? Correct: Your answer is correct. . (c) What is the average power delivered to the light bulb? Correct: Your answer is correct. . W

Solution

Here ,

I = 1.414 * sin(31.4 t)

a) I = Io * sin(2 *pi * f * t)

comparing , 2*pi * f = 31.4

f = 5 Hz

the frequency of alternatiung current is 5 Hz

b)

let the resistance is R

Using Ohm\' law

R = Vrms/Irms

R = 120/(1.414/1.414)

R = 120 Ohm

the resistance is 120 Ohm

c)

average power delivered to the light bulb = Irms * Vrms

average power delivered to the light bulb = 1 * 120 W

average power delivered to the light bulb = 120 W

the average power delivered to the light bulb is 120 W