A video clip of this demonstrate is accessible at this link.
You are watching: How much power is dissipated in a light bulb that is normally rated at 75 w
OK. These are actually AC circuits. Because the loads are almost purely resistive, i.e., there room no capacitances or inductances (or castle are tiny enough to be negligible), and since the rms (root-mean-square) AC voltage and also current law in purely resistive circuits as DC voltage and current do, the 2 circuits shown over are indistinguishable to the corresponding DC circuits. The AC from the wall surface is sinusoidal. The rms voltage because that a sinusoid is 0.707Vp, whereby Vp is the optimal voltage. Similarly, the rms current through a resistor is 0.707ip, where ip is the optimal current. These effective values correspond come the DC values that would give the exact same power dissipation in the resistor. These room slightly various from the average voltage and current, which are 0.639Vp and also 0.639ip because that a sinusoid. For AC indigenous the wall, the rms voltage is around 120 V, and the mean voltage is around 110 V.
Each board has three 40-watt bulbs, associated as shown by the resistor circuit painted on it. The plank on the left has the bulbs arranged, that course, in parallel, and the plank on the right has actually them in series. Since power, P, equals iV, P/V = i, so at 120 V, a 40-watt bulb draws 1/3 A. (The systems in iV room (C/s)(N-m/C), or J/s, which space watts.) for a given resistance, V = iR, for this reason the bulb’s resistance (when it has actually 120 volts across it) is 120/(1/3), or 360 ohms. (We also know through the two equations above that p = i2R, which offers R together 40/(1/9), or 360 ohms.)
When the bulbs are connected in parallel, each bulb has 120 V throughout it, each draws 1/3 A, and each dissipates 40 watts. In this circuit, every bulbs glow in ~ their complete brightness. The full power dissipated in the circuit is 3 times 40, or 120 watts (or 3(1/3) A × 120 V = 120 W).
In the collection circuit, any type of current that flows v one bulb need to go through the other bulbs together well, for this reason each pear draws the very same current. Due to the fact that all 3 bulbs are 40-watt bulbs, they have actually the very same resistance, therefore the voltage drop across each one is the same and equals one-third the the used voltage, or 120/3 = 40 volts. The resistance of a light pear filament transforms with temperature, however if we ignore this, we have the right to at least about estimate the present flow and power dissipation in the collection circuit. We have actually 120 V/(360 + 360 + 360) ohms = 1/9 A. The strength dissipated in each pear is either (1/9)2 × 360 = 4.44 watts, or (1/9) × 40 = 4.44 watts. The full power dissipated in the circuit is 3 times this, or 13.3 watts ((1/9)2 × 3(360) = 1080/81 = 13.3 W, or (1/9) A × 120 V = 13.3 W).
With fresh light bulbs, direct measurement v an ammeter reflects that the actual current flowing in the parallel circuit is 0.34 A because that one bulb, 0.68 A for two bulbs and also 1.02 A for 3 bulbs, and also in the collection circuit that is 0.196 A. For this reason the current, and thus the dissipated strength (23.5 watts), in the collection circuit are virtually twice what we arrived on above.
An “ohmic” resistance is one that stays consistent regardless of the used voltage (and thus likewise the current). If the light bulbs behaved this way, the measured existing in the series circuit would certainly agree with the calculation above. Even though they perform not, this demonstration offers a good sense of the difference in actions between a collection and parallel circuit made v three the same resistors.
What wake up if the irradiate bulbs space not all of the very same wattage rating?
An exciting variation of this demonstrate is to show what happens as soon as we put light bulbs the three various wattages in each circuit. A an excellent choice is to save one 40-W light bulb in each circuit, and also then include a 60-W bulb and a 100-W bulb. In the parallel circuit, as detailed above, the voltage across each pear is the exact same (120 V), therefore each pear draws the current that it would if it alone were connected to the wall, and the intensities that the bulbs for this reason vary together you would suppose from the wattage ratings. The 100-W bulb is the brightest, the 40-W pear is the dimmest, and also the 60-W pear is what in between. Once we placed the same mix of bulbs in series, an interesting thing happens. Since both the 60-W bulb and the 100-W bulb have actually lower resistance 보다 the 40-W bulb, the current through the circuit is somewhat higher than because that the three 40-W light bulbs in series, and the 40-W bulb glows much more brightly 보다 it did when it was in series with two various other 40-W bulbs. The current through this circuit steps 0.25 A. This is about 76% that the 0.33 A the the 40-W pear would draw by itself, fifty percent the 0.5 A that the 60-W bulb would certainly draw, and also 30% the the 0.83 A that the 100-W bulb would draw. In ~ this current, the 40-W pear lights fairly brightly, the 60-W bulb just barely glows, and also the 100-W bulb does not light at all. The photograph below shows the operation of these two circuits:
The bulbs in each circuit, native left come right, room a 40-W, 60-W and also a 100-W light bulb. In the parallel circuit, the bulbs obviously increase in brightness from left to right. In the collection circuit, the brightness decreases indigenous left to right. The measured voltages in the circuit are 120 V throughout all 3 bulbs, 109 V throughout the 40- and the 60-W bulbs, and 78 V throughout the 40-Watt bulb. The voltage drop throughout the 60-W pear is therefore 31 V, and it is 11 V throughout the 100-W bulb. Multiplying every of these by the 0.25-A current, we find that in the collection circuit, the 40-W bulb dissipates about 20 watts, the 60-W pear dissipates 7.8 watts, and also the 100-W bulb dissipates around 2.8 watts, which corresponds with the loved one intensities we observe for the three bulbs.
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1) Howard V. Malmstadt, Christie G. Enke and also Stanley R. Crouch. Electronics and also Instrumentation for Scientists (Menlo Park, California: The Benjamin/Cummings publishing Company, Inc., 1981), pp. 31-32.