Consider the circuit shown below. Find V1, V2, and R4. |...

Name: Problem 39, Chapter 10: University Physics
Uploaded: 2020-06-30T07:44:46-08:00
Duration: 6 min 1 s
Channel: Ren Jie Tuieng
Description: Consider the circuit shown below. Find V1, V2, and R4.

Key Concepts

Kirchhoff's Laws

These fundamental principles, including Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL), are essential for circuit analysis. KVL states that the sum of voltage drops around any closed loop in a circuit must equal zero, while KCL states that the total current entering a node must equal the total current leaving that node. They provide the basis for formulating the necessary equations to solve for unknown variables in a circuit.

Node Voltage Analysis

This technique involves assigning voltage variables to the nodes of a circuit relative to a common reference point (ground) and applying KCL to derive a system of equations. It is particularly useful for finding unknown node voltages such as V1 and V2, simplifying the analysis of complex circuits by reducing the number of equations required.

Ohm's Law

Ohm's Law, expressed as V = IR, relates the voltage across a resistor to the current flowing through it and its resistance. This fundamental relationship is used to connect the voltage drops in the circuit components and is pivotal when writing the equations that describe the circuit behavior.

Resistor Network Simplification

Understanding how to combine resistors, either in series or parallel, is key to reducing complex circuits into simpler equivalents. Simplification of resistor networks aids in analyzing circuits and can be crucial when determining an unknown resistor value, such as R4, by using equivalent resistance concepts in the overall network configuration.

Transcript

00:01 For this question we have this following figure and we want to identify the unknowns which are r4, v1 and v2.

00:13 Now at first glance this is actually seemed like quite a complicated circuit and don't know where to start but we're going to use kerchov's rule very simply and we want to make use of all the information that we know.

00:30 So the control rule is the loop rule that we're going to use that a closed loop must have a total potential difference or potential across the entire loop must be zero.

00:46 So we're going to choose our loops wisely such that we have as little unknown as possible.

00:52 And if possible, we have one unknown for each loop in order to get our answer very quickly.

00:58 So looking at r4 over here, one of the loop that contains r4 as the only unknown is this loop over here, this loop.

01:21 The outer loop encompassing just these two boxes over here.

01:29 And if you are to just follow the entire loop in this clockwise side.

01:34 Manner, there's no other unknown except for r4.

01:38 So we can solve for our 4 just by using this single loop.

01:44 So let's go through this entire loop, right? so first off we pass through r2 in the opposite direction to our current.

01:53 So we've got to add that up.

01:55 Right, that will be positive.

01:58 So there will be r2 which is 4 oms multiplied by 3 ampiers.

02:05 And then we bypass r3 and i3 in the opposite direction to the current.