La figura P11.4 muestra tres lámparas conectadas a un...

La figura P11.4 muestra tres lámparas conectadas a un voltaje de CA doméstico de $120 \mathrm{~V}$ CA (rms). Las lámparas 1 y 2 tienen una potencia de $150 \mathrm{~W}$, y la lámpara 3 tiene una potencia de $100 \mathrm{~W}$. Hallar (a) la corriente rms y (b) la resistencia de cada lámpara. (c) ¿Cuál es la resistencia total de la combinación de las tres lámparas? FIGURE CAN'T COPY. Para ver las figuras a color, acceda al código

La figura P11.4 muestra tres lámparas conectadas a un voltaje de CA doméstico de $120 \mathrm{~V}$ CA (rms). Las lámparas 1 y 2 tienen una potencia de $150 \mathrm{~W}$, y la lámpara 3 tiene una potencia de $100 \mathrm{~W}$. Hallar (a) la corriente rms y (b) la resistencia de cada lámpara. (c) ¿Cuál es la resistencia total de la combinación de las tres lámparas?
FIGURE CAN'T COPY.
Para ver las figuras a color, acceda al código

Key Concepts

Power in Resistive Circuits

In purely resistive AC circuits, the power can be determined using the relation P = V²/R. This connection between power, voltage, and resistance is crucial for calculating either resistance or current when power ratings and voltage (rms) are given.

Parallel Circuit Analysis

In circuits where multiple resistive elements are connected in parallel, each element experiences the same voltage across it. The total or equivalent resistance is found by taking the reciprocal of the sum of the reciprocals of the individual resistances, which is key for evaluating overall circuit behavior.

AC RMS Voltage

The rms voltage in AC circuits is the effective voltage that produces the same heating effect as an equivalent DC voltage. It is used to calculate power consumption and other circuit parameters when dealing with alternating current.

Ohm's Law

Ohm's Law is a fundamental relation in electrical circuits that connects the voltage, current, and resistance by the equation V = IR. It allows for the determination of one variable when the other two are known, essential for analyzing both AC and DC circuits.

Transcript

00:01 One of the most straightforward circuits to deal with in an ac setting is a household circuit where everything is in parallel and one in which you only have resistors.

00:15 What is true in such a case is that the average power that is dissipated by each resistor is the rms current, root mean square current, going through the resistor.

00:31 And i'll put this as a delta v.

00:34 Rms, indicating that it is an amplitude of some sort.

00:40 So let's take a look at an example.

00:43 Well, before we do the example, i do want to point out that the voltage through a resistor is in phase with the current through it.

00:55 And we have the omslaw relationship that irms is equal to delta v.

01:07 Rms divided by the resistance.

01:12 So as an example, let's take a look at the circuit above with three light bulbs, which can be essentially treated as light as resistors.

01:28 They aren't perfect resistors because they do change resistance as they heat up, but we'll assume that they've been lit for a while and have stabilized.

01:41 But we know the power average used by each light bulb, so that is usually what is given stamped on the light bulb.

01:50 So we'll call them bulbs 1, 2, and 3, just so we have a distinction there.

01:58 But bulb number 1, we can think about the current through it is simply the power 150 watts, divided by 120 volts.

02:13 So that's 1 .25 amps.

02:15 And likewise for bulb number two.

02:20 What is true is that the current going through each of those bulbs and i'll show it's a straight line, but of course it's oscillating.

02:31 It's also 150 watts divided by 120 volts.

02:40 Whereas for the third bulb, we simply do the same thing, but with 100 watts.

02:58 And that goes intuitively with the idea that the higher wattage bulb is going to have to have more current going through it...

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