It does add up, though. 4.17(a), a certain amount of heat is produced in the resistor in a given time.

In general, the rms value of any function with period T has an effective value given byIf the function consists of a number of sinusoidal terms, that isThe peak factor of any waveform is defined as the ratio of the peak value of the wave to the rms value of the wave.From factor of a waveform is defined as the ratio of rms value to the average value of  the wave.From factor of a sinusoidal waveform can be found from the above relation. Using only half a cycle, as illustrated in fig 1.2.3 the average value (voltage or current) is always 0.637 of the peak value of the wave.

rMs and peak Values in sine Wave ac power: As explained above, in a sine wave, the values of AC voltage (Volt, V) and current (Ampere, A) vary with time. rf-power math voltage. 4.12. The average value of a sine-shaped voltage or current is 0. Dan Dan. However, if the starting power of pumps is relatively large, the power frequency inverters with more than twice the power are usually purchased. The power supplied to a circuit by a battery is calculated using P = VI. 4.17(b). asked Oct 23 '13 at 22:31.

share | improve this question | follow | edited Oct 23 '13 at 23:36. An example...if a 100 W light bulb is on for two hours each day, and energy costs $0.10 per kW-h, how much does it cost to run the bulb for a month? In many cases, Joule heating is wasted energy. Here the peak to peak value is 8 V.In general, the average value of any function υ(t), with period T is given byThat means that the average value of a curve in the X- Y plane is the total area under the complete curve divided by the distance of the curve. These are instantaneous, peak, peak to peak, root mean square (rms) and average values.Consider the sine wave shown in Fig. If the average of the full cycle was taken it would of course be zero, as in a sine wave symmetrical about zero, there are equal excursions above and below the zero line. Cost = 0.1 kW x 60 hours x $0.1/kW-h = $0.6, or 60 cents. 1 W = 1 J/s

So the average value of a sine wave is defined over a half-cycle, and not a full cycle period.The average value of the sine wave is the total area under the half-cycle curve divided by the distance of the curve.The average value of a sine wave is shown by the dotted line in Fig. Now you average those values, obtaining 36 / 4 = 9. Batteries and power supplies supply power to a circuit, and this power is used up by motors as well as by anything that has resistance. Power is the rate at which work is done. Appliances that use energy most efficiently sometimes cost more but in the long run, when the energy savings are accounted for, they can end up being the cheaper alternative. If you need to know about the average power used, it is the rms values that go into the calculation. The peak to peak value of a sine wave is the value from the positive to the negative peak as shown in Fig. Average value sine wave. The values of the rated output voltage and current of an AC power source are specified in RMS values. Cost = (Power rating in kW) x (number of hours it's running) x (cost per kW-h) To find the rms average, you square everything to get 1, 1, 9, and 25. Anything you plug into a wall socket runs at 120 V, so if you know that and the current you can figure out how much power it uses. The current that comes from a wall socket, on the other hand, is alternating current. Because the voltage varies sinusoidally, with as much positive as negative, doing a straight average would get you zero for the average voltage. The graph above shows voltage as a function of time, but it could just as well show current as a function of time: the current also oscillates at the same frequency. In Fig.

That's actually a kind of average of the voltage, but the peak really is about 170 V.) This oscillating voltage produces an oscillating electric field; the electrons respond to this oscillating field and oscillate back and forth, producing an oscillating current in the circuit.

With alternating current, the current continually changes direction. (You might think this value of 170 V should really be 110 - 120 volts.

For a wall socket in North America, the voltage changes from positive to negative and back again 60 times each second. 4.15.The root mean square (rms) value of a sine wave is a measure of the heating effect of the wave. 4.14. If the circuit has capacitors, which store charge, the current may not be constant, but it will still flow in one direction. Doing this for a sine wave gets you an rms average that is the peak value of the sine wave divided by the square root of two. Finally, take the square root to get 3. This average value we use for the voltage from a wall socket is known as the root mean square, or rms, average. The cost for power that comes from a wall socket is relatively cheap. On the other hand, the cost of battery power is much higher. Otherwise, because the starting power of the pump can reach 5000W-7000W, it will cause insufficient power and can not start. The power dissipated in a resistor goes into heating the resistor; this is know as Joule heating. It has units of Watts.