What Determines the Current in an AC Circuit with a Light Bulb?

[Fazza3_uae]

The current in the circuit ...??

Homework Statement

An AC voltage of the form V = V_max sin 2*pi*f*t , with frequency 22 Hz and maximum voltage 763 V, is applied across a 17 W light bulb. When the voltage is first applied.

a) what is the current through the circuit?

Three Choices :

1. the maximum current
2. 0
3. the rms current

What is the correct answer and why ... ??


b) When t = T/4 , where T is the period of the applied voltage, what is the current in the circuit?

Homework Equations

P = I * V
I _max = $$\sqrt{}2$$ * I _rms
T = 1/f

The Attempt at a Solution

In part a) i think that when the voltage is first applied means that time is ZERO so it could be ZERO the options # 2

In part b) I substituted t = 0.25T or 0.25/f in this formual

V = Vmax sin 2*pi*f*t

I found V then I used P = I * V and solved for I but i got wrong answer.

 

[willem2]

17 W is the average power over a full cycle. It's equal to $I_{rms} V_{rms}$. You used this value as if it was the instantaneous power at t=0.25T

 

[kerimek]

I would like to clarify and provide a more detailed response to the given content.

Firstly, the question states that an AC voltage with a frequency of 22 Hz and maximum voltage of 763 V is applied across a 17 W light bulb. This implies that the light bulb is connected in series with the AC voltage source, forming a circuit. In this circuit, the AC voltage source is the driving force that causes the flow of electrons, also known as electric current.

a) The question asks for the current through the circuit when the voltage is first applied. This means at the initial moment when the voltage is turned on, and the circuit is closed. At this moment, the voltage is at its maximum value, and the current through the circuit will also be at its maximum value. This is because the current in a circuit is directly proportional to the voltage applied, as stated in Ohm's Law (I = V/R). Therefore, the correct answer would be option 1, the maximum current.

b) Now, when t = T/4, where T is the period of the applied voltage, the voltage has decreased to one-fourth of its maximum value. This means that the current in the circuit will also decrease accordingly. To calculate the current at this particular moment, we can use the formula I = V/R, where V is the voltage at that moment and R is the resistance of the light bulb. The resistance of the light bulb can be calculated using the formula P = I^2 * R, where P is the power of the light bulb, given as 17 W. By substituting the values, we can find the current at t = T/4. The correct answer would be the rms current, option 3, as it takes into account the changing values of the current in an AC circuit.

In conclusion, as a scientist, it is essential to understand the fundamental concepts and laws related to electricity and circuits to provide accurate and detailed responses to such questions. It is also crucial to pay attention to the given information and carefully analyze the question to arrive at the correct answer.