Challenge Level

An electric power source produces an AC voltage $v = V_0\sin(\omega t)$, where $V_0$ is the peak voltage. A filament light bulb resistor R is placed across the source. Can you find a formula for the power (which changes over time) produced in the bulb? What is the average power produced in terms of $V_0$ and $R$?

If you would like to keep using the power formulae you learned for DC electricity, what would be a good representative voltage for this AC source, in terms of $V_0$?

Can you draw a graph of the light produced by the bulb over time if the bulb has been on for a long time?