The current through a 50-? resistor is I = (0.80 A) sin(240 t ), where t is meas

Question

The current through a 50-? resistor is I = (0.80 A) sin(240t), where t is measured in seconds. How much power on average is dissipated in the resistor?

We are given a tip that max current (I0) is 0,80 A but I am not sure why because I = (0.80 A) sin(240t). Wouldn't max current equal the the result of this equaion not just the 0.80 A?

Power on average = IrmsVrms so I figure the first thing to do is calculate for the Irms value using the 0.80 A since it was told to us it is the max current.

Irms = I0/square root of 2 = 0.80/square root of 2 = .5656854249 A

Now I get even more confused becaause we were told to use I2rmsR to get the power disipated in the resistor. So, we are not going to use the Power on Average equation at all apparently. So, I used the given claculation to get

PDisipated = I2rmsR = (.56568542492 A)(50-?) = 16 W

This matches one of the multiple choice answer but not sure if correct. If I am right, can you explain why we just use 0.80 A as max current and not the resukt of the entire given equation for I in the question? Also, how is that PDisipated = I2rmsR derived? I would never figure this out if not given to us because it is not in the textbook or classroom examples.

Explanation / Answer

1)

Ya, for your first doubt of I = 0.8*sin(240t) is genuine. and the maximum value should be from this equation.But if you see the equation properly. current(I) in this equation has two components :

a)the amplitude , which is 0.8A which remains constant for any t

and

b) the variable part sin(240t) which changes with time. But the maximum value of sine function is 1 .

So, the product of 0.8*sin(240t) will have maximum of 0.8*1 = 0.8 A

So, as a shortcut, we only see the amplitude part to be the maximum value of current.

2)

You can use any of the equation to solve your question

To start with, P = Irms*Vrms

But , Vrms = Irms*R

So, P = Irms*(Irms/R) = (Irms)^2/R

So, Prms = Irms*Vrms = Irms^2/R <-----------both are same

3)

Yes your answer is right for Pdissipated

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.