The problem involves calculating the energy dissipated in a resistor with a specified resistance and a voltage function over a given time interval. The subject area pertains to electrical circuits and energy calculations.
The discussion is ongoing, with participants providing hints and guidance on the correct approach to integrate the voltage function to find energy. There is recognition of the need to clarify the relationship between power and energy, and multiple interpretations of the integration process are being explored.
Participants are navigating the constraints of the problem, including the need for correct units and the specific form of the voltage function. There is an emphasis on ensuring that the calculations align with the physical principles governing energy dissipation in resistors.
I integrated this V(t) = 6sin(10t+pi/4)*exp(-2t)DrDu said:Definite integral sounds good, the question is which integral exactly?
NoDrDu said:Does the integral ##\int V(t) dt ## have the dimension of an energy?
I think the answer should be in joules as its asking for energy dissipated.phyzguy said:Also, the units of the answer should be supplied.
Bob jefferson said:I think the answer should be in joules as its asking for energy dissipated.
so i just multiply 0.5s with the value i obtained from the integration.gneill said:Hint: Energy is the time integral of power.
No, you need to perform another integration where what you are integrating is the instantaneous power.Bob jefferson said:so i just multiply 0.5s with the value i obtained from the integration.
Oh so actually putting V^2/r in the integral.gneill said:No, you need to perform another integration where what you are integrating is the instantaneous power.
Bob jefferson said:Oh so actually putting V^2/r in the integral.
so would it be some thing like ##\frac 1 R \int_0^{0.5} V^2(t) dt ##gneill said:No, you need to perform another integration where what you are integrating is the instantaneous power.
Bob jefferson said:so would it be some thing like ##\frac 1 R \int_0^{0.5} V^2(t) dt ##
so i need a bit of guidance, would ##sin^2(10t+\frac \pi 4)## equal to ##\frac 1 2(1-cos(2*10t+\frac \pi 4))##phyzguy said:Yes.