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

You are watching: What is the resistance of a 120-w incandescent lamp connected to a 120-v power supply?

OK. These are actually AC circuits. Because the lots are almost purely resistive, *i.e.*, there are no capacitances or inductances (or castle are small enough to it is in negligible), and also since the rms (root-mean-square) AC voltage and also current behave in completely resistive circuits together DC voltage and current do, the 2 circuits shown above are equivalent to the corresponding DC circuits. The AC indigenous the wall surface is sinusoidal. The rms voltage because that a sinusoid is 0.707Vp, wherein Vp is the height voltage. Similarly, the rms existing through a resistor is 0.707*i*p, wherein *i*p is the optimal current. This *effective* worths correspond come the DC values that would provide the same power dissipation in the resistor. These space slightly various from the *average* voltage and also current, which space 0.639Vp and also 0.639*i*p because that a sinusoid. Because that AC native the wall, the rms voltage is roughly 120 V, and the average voltage is around 110 V.

Each board has actually three 40-watt bulbs, linked as presented by the resistor circuit painted ~ above it. The plank on the left has actually the bulbs arranged, the course, in parallel, and also the board on the right has actually them in series. Because power, P, equates 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 are watts.) for a offered resistance, V = *i*R, therefore the bulb’s resistance (when it has 120 volts across it) is 120/(1/3), or 360 ohms. (We also know by the 2 equations above that p = *i*2R, which provides R together 40/(1/9), or 360 ohms.)

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

In the collection circuit, any current that flows v one bulb should go through the other bulbs as well, so each bulb draws the same current. Due to the fact that all 3 bulbs are 40-watt bulbs, they have the very same resistance, for this reason the voltage drop throughout each one is the same and equals one-third the the applied voltage, or 120/3 = 40 volts. The resistance of a light pear filament changes with temperature, however if we overlook this, we deserve to at least roughly estimate the existing flow and power dissipation in the series circuit. We have actually 120 V/(360 + 360 + 360) ohms = 1/9 A. The strength dissipated in each bulb is either (1/9)2 × 360 = 4.44 watts, or (1/9) × 40 = 4.44 watts. The complete power dissipated in the circuit is 3 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 light bulbs, direct measurement with an ammeter shows that the actual present flowing in the parallel circuit is 0.34 A because that one bulb, 0.68 A for 2 bulbs and 1.02 A for 3 bulbs, and also in the collection circuit it is 0.196 A. Therefore the current, and thus the dissipated power (23.5 watts), in the series circuit are nearly twice what we landed on above.

An “ohmic” resistance is one that stays continuous regardless of the used voltage (and thus also the current). If the light bulbs behaved this way, the measured existing in the collection circuit would certainly agree with the estimate above. Also though they execute not, this demonstration offers a good sense that the distinction in behavior between a collection and parallel circuit made through three identical resistors.

**What happens if the light bulbs room not all of the same wattage rating?**

An exciting variation the this demonstration is to present what happens when we placed light bulbs of three various wattages in each circuit. A good choice is to store one 40-W light bulb in each circuit, and also then include a 60-W bulb and also a 100-W bulb. In the parallel circuit, as provided above, the voltage across each pear is the exact same (120 V), therefore each bulb draws the current that it would certainly if the alone were connected to the wall, and the intensities that the bulbs for this reason vary as you would intend from the wattage ratings. The 100-W pear is the brightest, the 40-W bulb is the dimmest, and the 60-W pear is somewhere in between. As soon as we put the same combination of bulbs in series, an interesting thing happens. Due to the fact that both the 60-W bulb and the 100-W bulb have 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 pear glows an ext brightly than it did once it to be in collection with two various other 40-W bulbs. The present through this circuit measures 0.25 A. This is about 76% the the 0.33 A the the 40-W bulb would draw by itself, half the 0.5 A that the 60-W bulb would certainly draw, and 30% that the 0.83 A the the 100-W bulb would draw. At this current, the 40-W bulb lights relatively brightly, the 60-W bulb just barely glows, and the 100-W pear does not light at all. The photograph listed below shows the operation of these 2 circuits:

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

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**References:**

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