What is the value of current through the 12-ohm resistor in the problem 14circuit diagram?

Name: Problem 18, Chapter 5: Electricity 1: Devices, Circuits and Materials
Uploaded: 2021-07-05T21:34:37-08:00
Duration: 5 min 45 s
Channel: Meghan Miholics
Description: What is the value of current through the 12-ohm resistor in the problem 14circuit diagram?

What is the value of current through the 12-ohm resistor in...

Key Concepts

Kirchhoff's Circuit Laws

Kirchhoff's Circuit Laws, including the current law (KCL) and voltage law (KVL), provide essential tools for analyzing complex circuits. KCL states that the total current entering a junction equals the total current leaving it, while KVL states that the sum of the voltage drops around any closed loop must equal zero, allowing for systematic determination of unknown currents and voltages.

Current Division

Current division is a technique used in circuits with parallel branches to determine the proportion of current flowing through each branch based on the resistances of the branches. This concept is important when isolating the current through a specific resistor within a parallel network.

Ohm's Law

Ohm's Law is a fundamental concept in electrical circuits that relates voltage, current, and resistance. It states that the voltage across a resistor is equal to the current flowing through it multiplied by its resistance, and it serves as the basis for calculating circuit parameters in resistor networks.

Resistor Networks

Resistor networks involve the arrangement of resistors in series and parallel configurations. Understanding the combination of resistors helps in determining the equivalent resistance of the network, which is crucial for analyzing how current flows through different parts of the circuit.

Transcript

00:01 In this question, we are asked to look at the circuit in figure 2129 and suppose that we connect a 12 -volt battery to the points a and b.

00:10 We're then asked to comment on if the current in the 45 -oam resistor is greater than less than or the same as the current in the 35 -am resistor, and then to calculate the current flowing through each of their three resistors in the circuit.

00:24 So first of all, i'm just going to start off by drawing the complete circuit.

00:28 Yep.

00:29 So we've got the 12 -volt battery, and that's connected to the three resistors.

00:37 And we do have two branches here, one with two resistors, and then another with a single resistor.

00:49 So here we've got 35 oms, here is 45 oms, and then the last one is 82 oms.

01:01 Now, according to kirchhoff's laws, we know that the total current in the battery is going to, sorry, the total current in the circuit is going to come out of the battery and into this junction point and it's going to split.

01:20 So we're going to have some current going down the one branch and some current going down the other branch.

01:27 In terms of figuring out how much current will go down each branch, we have to consider the total.

01:32 Total resistance on each branch.

01:34 So on the right hand branch, the way i've drawn it here, we have 45 oms of resistance.

01:40 On the left hand branch, we have 35 plus 82 oms of resistance.

01:46 So in total, that branch is going to have a lot more resistance on it than the other branch.

01:59 So in total, that's going to be 117 oms.

02:02 So we know that the current is going to go down the path or more of the current is going to go down the path of lesser resistance.

02:10 So there's going to be more current in the 45 -oam branch than in the other branch.

02:16 Okay, so more current in the 45 -on resistor than the 35 -oom resistor...

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