Using the circuit in Figure 4-10, what is the current through the 10 -ohm resistor?

Name: Problem 14, Chapter 4: Electricity 1: Devices, Circuits and Materials
Uploaded: 2022-03-23T03:13:27-08:00
Duration: 4 min 16 s
Channel: Ekaveera Kumar
Description: Using the circuit in Figure 4-10, what is the current through the 10 -ohm resistor?

step 1 So, let us form the mesh currents something like this. So this is I1 and let's take this as I2 a

Using the circuit in Figure 4-10, what is the current...

Key Concepts

Circuit Analysis Techniques

Circuit analysis techniques include methods such as nodal analysis, mesh analysis, and the use of equivalent circuits. These techniques allow engineers to systematically analyze the behavior of electrical circuits by breaking them down into simpler parts, thus facilitating calculations like determining the current through specific components, such as a resistor, by reducing complex networks into manageable forms.

Series and Parallel Resistor Combinations

In circuit analysis, resistors can be arranged in series or in parallel, and each arrangement affects the overall resistance differently. In a series configuration, resistances add directly, resulting in a higher total resistance, while in a parallel configuration, the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances, often reducing the overall resistance. Understanding these combinations is key to simplifying circuits and accurately determining current distribution through components.

Ohm's Law

Ohm's Law is a fundamental principle in electrical engineering that relates voltage, current, and resistance. It states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. This concept is essential for calculating unknown quantities in any circuit, such as determining the current through a resistor when the voltage and resistance are known.

Kirchhoff's Laws

Kirchhoff's Laws include Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL). KVL states that the sum of the electrical potential differences around any closed network is zero, while KCL asserts that the sum of currents entering a node equals the sum of currents leaving the node. These laws are crucial for analyzing complex circuits where multiple loops or nodes are involved, allowing for the establishment of equations that model the circuit behavior.

Transcript

00:01 So, let us form the mesh currents something like this.

00:04 So this is i1 and let's take this as i2 and let's take this as i3.

00:16 Our aim is to find i2 because i2 is the current that is flowing in 10 over system, right? now let's form a resistance matrix.

00:25 The resistance matrix into i1, i2, i3 is equal to the respective driving voltages.

00:35 What is the resistance matrix? the first element will be some of all the resistances in the first mesh.

00:43 What are the resistance is in the first mesh? 4 -7 -92 at 30 rooms.

00:52 What is the resistance common to first and second mesh? it's 4 -homes and in that 4 -homes, i -1 is coming in one direction, i -2 is coming in the opposite direction, so it's negative 4.

01:04 What is the resistance in common to mesh 1 mesh 3? it is 7.

01:11 In 7 oms, ivan is coming down and ip3 is coming up.

01:15 So it's negative 7.

01:17 And since the resistance matrix is a symmetric matrix, this minus 4 will come here.

01:23 This minus 7 will come here.

01:26 And this element will be some of all the resistances on the second mesh.

01:32 That is 10 4 to 16.

01:36 And what is the common resistance between mesh 2 and mesh 3? it's basically negative 2 because i3 and i2 are in opposite directions...