 A video of this demonstrate is accessible at this link.

You are watching: A 60-w light bulb connected to a 120-v source draws a current of

OK. These room actually AC circuits. Since the loads are practically purely resistive, i.e., there are no capacitances or inductances (or lock are small enough to be negligible), and also since the rms (root-mean-square) AC voltage and also current act in purely resistive circuits as DC voltage and current do, the 2 circuits shown over are equivalent to the corresponding DC circuits. The AC from the wall surface is sinusoidal. The rms voltage for a sinusoid is 0.707Vp, whereby Vp is the optimal voltage. Similarly, the rms current through a resistor is 0.707ip, wherein ip is the optimal current. These effective worths correspond come the DC values that would provide the same power dissipation in the resistor. These are slightly different from the average voltage and also current, which room 0.639Vp and also 0.639ip for a sinusoid. Because that AC indigenous the wall, the rms voltage is around 120 V, and the average voltage is around 110 V.

Each board has actually three 40-watt bulbs, associated as presented by the resistor circuit painted top top it. The plank on the left has actually the bulbs arranged, the course, in parallel, and also the plank on the right has actually them in series. Since power, P, equals iV, P/V = i, so in ~ 120 V, a 40-watt bulb draws 1/3 A. (The systems in iV space (C/s)(N-m/C), or J/s, which are watts.) because that a offered 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 likewise know through the 2 equations over that p = i2R, which offers R as 40/(1/9), or 360 ohms.)

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

In the collection circuit, any kind of current the flows through one bulb must go with the various other bulbs as well, so each pear draws the same current. Due to the fact that all three bulbs are 40-watt bulbs, they have actually the same resistance, so the voltage drop across each one is the same and also equals one-third of the used voltage, or 120/3 = 40 volts. The resistance of a light bulb filament changes with temperature, yet if we overlook this, we have the right to at least roughly estimate the current flow and also power dissipation in the series circuit. We have actually 120 V/(360 + 360 + 360) ohms = 1/9 A. The power 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 watts ((1/9)2 × 3(360) = 1080/81 = 13.3 W, or (1/9) A × 120 V = 13.3 W).

With fresh light bulbs, straight measurement through an ammeter shows that the actual current flowing in the parallel circuit is 0.34 A for one bulb, 0.68 A for 2 bulbs and also 1.02 A for three bulbs, and in the collection circuit the is 0.196 A. So the current, and also thus the dissipated power (23.5 watts), in the collection circuit are virtually twice what we arrived on above.

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

What wake up if the light bulbs are not every one of the same wattage rating?

An amazing variation the this demonstrate is to show what happens as soon as we put light bulbs that three various wattages in every circuit. A an excellent choice is to keep one 40-W light bulb in every circuit, and then include a 60-W bulb and also a 100-W bulb. In the parallel circuit, as listed above, the voltage across each pear is the exact same (120 V), so each pear draws the current that it would if it alone were linked to the wall, and the intensities of the bulbs thus vary as you would expect from the wattage ratings. The 100-W pear is the brightest, the 40-W bulb is the dimmest, and also the 60-W pear is what in between. As soon as we put the same combination of bulbs in series, an amazing thing happens. Because both the 60-W bulb and also the 100-W bulb have lower resistance 보다 the 40-W bulb, the existing through the circuit is somewhat higher than because that the 3 40-W light bulbs in series, and also the 40-W pear glows much more brightly 보다 it did when it was in collection with two other 40-W bulbs. The present through this circuit measures 0.25 A. This is around 76% of the 0.33 A the the 40-W bulb would attract by itself, half the 0.5 A the the 60-W bulb would draw, and 30% that the 0.83 A that the 100-W bulb would certainly draw. At this current, the 40-W bulb lights reasonably brightly, the 60-W bulb simply barely glows, and the 100-W pear does not light in ~ all. The photograph below shows the operation of these 2 circuits: The bulbs in each circuit, native left to right, are a 40-W, 60-W and a 100-W light bulb. In the parallel circuit, the bulbs obviously increase in brightness indigenous left come right. In the series circuit, the brightness decreases indigenous left come right. The measure voltages in the circuit space 120 V across all 3 bulbs, 109 V across the 40- and the 60-W bulbs, and also 78 V throughout the 40-Watt bulb. The voltage drop throughout the 60-W bulb is for this reason 31 V, and it is 11 V across the 100-W bulb. Multiplying each of this by the 0.25-A current, we uncover that in the series circuit, the 40-W bulb dissipates around 20 watts, the 60-W bulb dissipates 7.8 watts, and the 100-W bulb dissipates around 2.8 watts, which corresponds with the loved one intensities we observe because that the 3 bulbs.

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References:

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