RMS value of alternating current
What direct current heats up as much as this alternating current?
Pass an alternating current and a direct current through identical resistors. If they produce the same heat in the same time, that DC voltage is called the effective (RMS) value of the AC voltage. For sinusoidal AC, the RMS value is 1/√2 of the peak value. The 220 V marked on household appliances is the RMS value; the peak is about 311 V.
Heat produced in the resistors
When the DC voltage equals the AC RMS value, the two curves meet at every whole period.
Think about it
A sinusoidal AC has a peak of 10 V. What DC voltage produces the same heat in the same resistor?
About 7.07 V, i.e. 10/√2. Set the DC voltage to around 7 V and the two heat curves nearly coincide; the AC curve is wavy because the instantaneous power varies between 0 and its maximum.
Model assumptionsResistance R = 10 Ω, independent of temperature · Frequency slowed to a fraction of a hertz so the lamp's brightening and dimming can be seen
Data log
Set the parameters and click “Record data”. Record several rows with different parameters to plot their relationship and fit a straight line; pause and record at different times to study how a reading changes with time.