Three identical light bulbs are connected in circuit to a...

Three identical light bulbs are connected in circuit to a battery, as shown in Figure $20-35$, Compare the level of brightness of each bulb when all the bulbs are illuminated. What happens to the brightness of each bulb if the following changes are made to the circuit? a. Bulb $A$ is removed from its socket. b. Bulb $C$ is removed from its socket c A wire is connected directly between points $D$ and $E$ d. A wire is connected directly between points $D$ and $E$

Three identical light bulbs are connected in circuit to a battery, as shown in Figure $20-35$, Compare the level of brightness of each bulb when all the bulbs are illuminated. What happens to the brightness of each bulb if the following changes are made to the circuit?
a. Bulb $A$ is removed from its socket.
b. Bulb $C$ is removed from its socket
c A wire is connected directly between points $D$ and $E$
d. A wire is connected directly between points $D$ and $E$

Key Concepts

Series Circuit

A series circuit is one in which components are connected end-to-end so that the same current flows sequentially through each component. In series circuits, any change, such as the removal of a component, interrupts the current flow throughout the entire circuit, thereby affecting the performance and brightness of devices like light bulbs.

Parallel Circuit

A parallel circuit is one in which components are connected across the same two points, so they each experience the same voltage from the power source. In parallel arrangements, the current is divided among the branches, and modifications to one branch (like removing a component) do not necessarily interrupt the operation of the others, though they do affect the overall current distribution and resistance.

Electrical Resistance and Brightness

The brightness of a light bulb depends on the power it dissipates, which is a function of the current through it and the voltage across it (as expressed by formulas like P = I²R or P = V²/R). The arrangement of bulbs—whether in series or parallel—determines the total circuit resistance, influencing the distribution of current and hence the brightness of each bulb.

Open Circuit

An open circuit occurs when a break is introduced into an electrical path, stopping the flow of current. Removing an element, such as a light bulb that interrupts the circuit, leads to an open circuit condition, which can cause all components in a series arrangement to lose power, affecting the brightness or causing the bulbs to go out.

Short Circuit

A short circuit is created when a low-resistance connection bypasses part of a circuit, allowing current to flow through an alternate path while avoiding a component. By connecting a wire directly across points in the circuit, the bypassed element effectively receives little or no current, altering the circuit’s overall resistance and the brightness of elements that remain in the circuit.

Transcript

00:01 Hello and welcome to chapter 18, problem number 22 of holt physics.

00:07 So in this problem, we're given a sort of graphic of three equivalent light bulbs hooked up to a battery.

00:14 And i think a difficult part of this question is really just converting that graphic to a recognizable circuit diagram that we're all familiar with.

00:22 But if you look at it, you'll see that b and c are connected in series, and then the b -c equivalent resistance is connected to a.

00:31 Via parallel connection.

00:33 So this is what's going to look like when you draw your circuit diagram with our points of interest, de and f.

00:39 And we also need to keep in mind that the brightness of each light bulb is going to depend on the power usage of each light bulb.

00:46 And we can manipulate the power usage with three different equations by changing our current voltage and resistance here.

00:55 So to start things off, it asks us what happens if we take out a in our circuit.

01:00 So right off the bat, we need to establish that a and then the b, c, equivalent resistance, they're going to share the same voltage.

01:09 So taking out a won't affect our voltage.

01:12 It will, however, affect our current because the current is not shared between components in parallel.

01:18 So if we look at p equals iv, we can see that our current goes up.

01:23 Therefore, b and c also go up in their brightness, and a is completely removed from the circuit, so it's not part of our question here.

01:32 Up next, it asks us what happens if we take out light bulbs c.

01:37 So the next important thing we need to look at is the fact that b, c, is an equivalent resistance.

01:45 So it's going to, taking out c, we'll change that r equivalent resistance here.

01:50 So we're going to use p equals v squared on r.

01:54 And we'll see that that that equivalent r is now just the resistance of b...

Please give Ace some feedback