A video clip of this demonstration is available at this link.

You are watching: A 100-w lamp glows brighter than a 25-w lamp. the electric resistance of the 100-w lamp is

OK. These space actually AC circuits. Due to the fact that the tons are almost purely resistive, *i.e.*, there space no capacitances or inductances (or they are small enough to it is in negligible), and since the rms (root-mean-square) AC voltage and current behave in purely resistive circuits together DC voltage and also current do, the 2 circuits shown over are indistinguishable to the equivalent DC circuits. The AC native the wall surface is sinusoidal. The rms voltage for a sinusoid is 0.707Vp, where Vp is the optimal voltage. Similarly, the rms existing through a resistor is 0.707*i*p, wherein *i*p is the height current. These *effective* worths correspond to the DC values that would provide the exact same power dissipation in the resistor. These room slightly various from the *average* voltage and also current, which room 0.639Vp and also 0.639*i*p because that a sinusoid. For AC from the wall, the rms voltage is around 120 V, and the typical voltage is about 110 V.

Each board has actually three 40-watt bulbs, associated as shown by the resistor circuit painted ~ above it. The plank on the left has the bulbs arranged, the course, in parallel, and also the plank on the right has them in series. Since power, P, amounts to *i*V, P/V = *i*, so at 120 V, a 40-watt bulb draws 1/3 A. (The systems in *i*V space (C/s)(N-m/C), or J/s, which room watts.) for a provided resistance, V = *i*R, for this reason the bulb’s resistance (when it has actually 120 volts across it) is 120/(1/3), or 360 ohms. (We likewise know through the two equations over that ns = *i*2R, which offers R together 40/(1/9), or 360 ohms.)

When the bulbs are connected in parallel, every bulb has 120 V throughout it, every draws 1/3 A, and each dissipates 40 watts. In this circuit, all bulbs glow in ~ their full brightness. The complete power dissipated in the circuit is 3 times 40, or 120 watts (or 3(1/3) A × 120 V = 120 W).

In the series circuit, any type of current that flows v one bulb have to go through the various other bulbs as well, for this reason each bulb draws the same current. Since all 3 bulbs space 40-watt bulbs, they have the exact same resistance, so the voltage drop throughout each one is the same and also equals one-third that the applied voltage, or 120/3 = 40 volts. The resistance of a light bulb filament changes with temperature, however if we overlook this, we deserve to at least around estimate the present flow and also power dissipation in the series circuit. We have actually 120 V/(360 + 360 + 360) ohms = 1/9 A. The strength dissipated in each pear is one of two people (1/9)2 × 360 = 4.44 watts, or (1/9) × 40 = 4.44 watts. The full power dissipated in the circuit is three times this, or 13.3 watt ((1/9)2 × 3(360) = 1080/81 = 13.3 W, or (1/9) A × 120 V = 13.3 W).

With fresh irradiate bulbs, direct measurement with an ammeter reflects that the actual existing flowing in the parallel circuit is 0.34 A for one bulb, 0.68 A for two bulbs and 1.02 A for 3 bulbs, and in the series circuit the is 0.196 A. Therefore the current, and also thus the dissipated power (23.5 watts), in the collection circuit are virtually twice what we landed on above.

An “ohmic” resistance is one that stays continuous regardless that the used voltage (and thus likewise the current). If the light bulbs behaved this way, the measured current in the series circuit would agree with the calculation above. Even though they do not, this demonstration provides a great sense that the distinction in actions between a series and parallel circuit made through three the same resistors.

**What wake up if the light bulbs room not all of the exact same wattage rating?**

An amazing variation that this demonstration is to show what happens when we put light bulbs of three different wattages in every circuit. A an excellent choice is to keep one 40-W light bulb in each circuit, and then add 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), so each pear draws the current that it would if that alone were linked to the wall, and the intensities of 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 combination of bulbs in series, an exciting thing happens. Since both the 60-W bulb and also the 100-W bulb have actually lower resistance than the 40-W bulb, the current through the circuit is somewhat higher than for the three 40-W light bulbs in series, and also the 40-W bulb glows much more brightly 보다 it did once it was in collection with two other 40-W bulbs. The existing through this circuit actions 0.25 A. This is about 76% the the 0.33 A that the 40-W pear would attract by itself, fifty percent the 0.5 A the the 60-W bulb would certainly draw, and also 30% that the 0.83 A that the 100-W bulb would certainly draw. In ~ this current, the 40-W bulb lights relatively brightly, the 60-W bulb just barely glows, and also the 100-W pear does no light at all. The photograph below shows the procedure of these 2 circuits:

The bulbs in each circuit, native left come right, are a 40-W, 60-W and a 100-W light bulb. In the parallel circuit, the bulbs obviously rise in brightness native left to right. In the series circuit, the brightness *decreases* native left to right. The measure voltages in the circuit room 120 V across all 3 bulbs, 109 V across the 40- and the 60-W bulbs, and 78 V across the 40-Watt bulb. The voltage drop throughout the 60-W bulb is for this reason 31 V, and also it is 11 V across the 100-W bulb. Multiplying each of these by the 0.25-A current, we discover that in the collection circuit, the 40-W pear dissipates around 20 watts, the 60-W pear dissipates 7.8 watts, and also the 100-W pear dissipates about 2.8 watts, which synchronizes with the family member intensities us observe because that the 3 bulbs.

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**References:**

1) Howard V. Malmstadt, Christie G. Enke and Stanley R. Crouch. *Electronics and also Instrumentation because that Scientists* (Menlo Park, California: The Benjamin/Cummings publishing Company, Inc., 1981), pp. 31-32.