Referring to Example 21-7 Suppose the three resistors in...

Referring to Example $21-7$ Suppose the three resistors in this circuit have the values $R_{1}=100.0 \Omega, R_{2}=200.0 \mathrm{f} 2,$ and $R_{3}=300.0 \mathrm{a},$ and that the emf of the battery is $12.0 \mathrm{V}$. (The re- $-$ sistor numbers are given in the Interactive Figure.) (a) Find the potential difference across each resistor. (b) Find the current that flows through each resistor.

Referring to Example $21-7$ Suppose the three resistors in this circuit have the values $R_{1}=100.0 \Omega, R_{2}=200.0 \mathrm{f} 2,$ and $R_{3}=300.0 \mathrm{a},$ and that the emf of the battery is $12.0 \mathrm{V}$. (The re- $-$ sistor numbers are given in the Interactive Figure.) (a) Find the potential difference across each resistor.
(b) Find the current that flows through each resistor.

Key Concepts

Ohm's Law

Ohm’s Law is a fundamental principle that relates the voltage across a resistor to the current flowing through it and its resistance by the equation V = I × R. This law is used to compute any one of the three quantities when the other two are known, and it is essential for analyzing circuits and solving for unknown values such as the potential difference across resistors and the currents flowing through them.

Kirchhoff’s Circuit Laws

Kirchhoff’s laws include the Voltage Law (KVL) and the Current Law (KCL). KVL states that the sum of the electric potential differences around any closed network is zero, which helps in determining the voltage drop across elements in a loop. KCL states that the total current entering a junction equals the total current leaving it, making it crucial for analyzing current distribution in circuits, especially when resistors are arranged in complex configurations.

Series and Parallel Resistor Combinations

Understanding how resistors combine in series and parallel is key in circuit analysis. In a series circuit, the total or equivalent resistance is the sum of individual resistances, while in a parallel circuit, the reciprocal of the equivalent resistance is the sum of the reciprocals of each resistor. This concept is crucial for simplifying circuit networks to calculate overall currents and voltage drops accurately.

Voltage Division

The voltage division principle allows for the determination of the voltage across individual resistors in a series circuit. It states that the voltage drop across a resistor in a series network is proportional to its resistance relative to the total resistance. This concept is heavily used when calculating the potential difference across each resistor in a circuit connected to a common voltage source.

Current Division

Current division is a technique used to determine the distribution of current among parallel branches in a circuit. It is based on the idea that the current entering a junction divides inversely proportional to the resistances of the parallel branches. This principle is important for finding the current through individual resistors when they are arranged in parallel configurations.

Transcript

00:01 In this problem, we'll use free cost loss to find the potential drop across each resistor and the current through each one.

00:07 So let's begin working with the potentials.

00:11 Now we know that throughout this outer branch, the potential drop has to add up to zero when we get to this point.

00:21 So that means that this resistor in this outer path experiences that 12 volts drop.

00:33 So we can say that the potential drop across resistor one are those 12 volts.

00:43 Now when we talk about these two, it's not that easy because now we have two resistors that experience each of them some potential drop that adds up.

00:58 So let's find that another way.

01:01 We know that a potential difference is going to be equal to the current times the resistance.

01:16 Therefore, we need to find the current for us to find the potential drop across each of the resistors.

01:24 So let's do that.

01:27 We have a potential drop of 12.

01:33 We have some current over here, and a total resistance.

01:42 That total resistance is the addition of these two resistors, 200 plus 300.

01:49 So that's 500.

01:52 So we know that the current is going to be.

01:54 Be 12 over 500 and that gives us 0 .024 amps now we know the current through this branch so now let's find the potentials we have second potential drop which is going to be equal to the resistance 200 oms times the current and that gives us a potential drop of 4 .8 volts therefore, potential number three is going to be 12 volts minus those 4 .8, because they have to add up to 0...

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