# Power in an AC Circuit Problem

1. Apr 17, 2015

### B3NR4Y

1. The problem statement, all variables and given/known data
The circuit in operates at 60 Hz with Emax = 170 V, and R = 4.5Ω .
How much energy is dissipated in the resistor in 0.75 s?
2. Relevant equations
P = VI
For a circuit like mine with only a power source and resistor, the current and voltage are in phase, so
V = E max sin (ωt)
and
$$I = \frac{E_{max} sin(\omega*t)}{R}$$

3. The attempt at a solution
Since I want to know the power dissipated over time, I took an integral $$V_{0} I_{0} \int_{0}^{t} sin(\omega t) dt$$
this should give me the total energy dissipated at time t, it doesn't, and I am not sure why.

2. Apr 17, 2015

### rude man

You ignored your own expressions for V and I in forming your integral ...

3. Apr 17, 2015

### B3NR4Y

oh, jeez, it should be
$$V_{0} I_{0} \int_{0}^{t} sin^{2}(\omega t) dt$$ ?

4. Apr 18, 2015

### rude man

Mucho better!

BTW the integral is easier if you write it as VoIo/ω ∫sin2(ωt)d(ωt) with limits 0 to ωt.
As if I'm not being picky enough, you should also use a dummy variable (like t') in the integral. ∫sin2(ωt')dt' with limits of 0 and t.