Need help with two questions, dealing with electricity

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To estimate the length of Nichrome wire needed for a heater using 400 W at 120 V, the resistance can be calculated using P = V^2/R, leading to R = 36 ohms. The length of the wire can then be determined based on its resistance per unit length. For the light bulb connected to a 120 V socket, the frequency of the alternating current is 314 Hz. The resistance of the bulb's filament can be calculated using the current formula, and the average power delivered to the bulb can be found using the appropriate power equations. Understanding these calculations is crucial for completing the assignment effectively.
Marcelgluch
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Hi, i have two questions from my assignment that i am having a very hard time understanding...

1. A piece of Nichrome wire has a radius of 6.5x10^-4 m. It is used in a laboratory to make a heater that uses 4.00x10^2 W of power when connected to a voltage source of 120 V. Ignoring the effect of temperature on resistance, estimate the necessary length of wire.


2.A light bulb is connected to a 120.0 V wall socket. the current in the bulb depends on the time (t) according to the relation I = (0.707 A)sin[(314Hz)t]. (a) what is the frequency of the alternating current? (b) determine the resistance of the bulb's filament. (c) what is the aaverage power deliever to the light bulb?


Could someone please help me out
 
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P=V2/R will help you.

I=I0sin(ωt)
 

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