Consider the circuit shown below. Write the three loop equations for the loops shown.

Name: Problem 42, Chapter 10: University Physics
Uploaded: 2020-07-01T02:27:21-08:00
Duration: 4 min 37 s
Channel: Ren Jie Tuieng
Description: Consider the circuit shown below. Write the three loop equations for the loops shown.

Consider the circuit shown below. Write the three loop...

Key Concepts

Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law is a fundamental principle in circuit analysis stating that the algebraic sum of all electrical potential differences around any closed loop in a circuit must be zero. This concept is essential for writing loop equations since it enables the formulation of equations that equate the voltage drops across individual components in a loop to the voltage sources present.

Mesh Analysis (Loop Analysis)

Mesh analysis, also known as loop analysis, is a systematic method used to determine the current flowing in each loop of a circuit. By applying Kirchhoff's Voltage Law to each mesh, one can derive a set of simultaneous equations where the unknowns represent the mesh currents. This method simplifies solving complex circuits by reducing them into a series of manageable equations.

Ohm's Law

Ohm's Law is a basic principle in electrical circuits that relates the voltage across an electrical component to the current flowing through it and its resistance. In the context of loop equations, Ohm's Law is used to express the voltage drop across resistive elements in terms of the current and resistance, facilitating the formulation and solution of the equations derived from Kirchhoff's Voltage Law.

Transcript

00:01 In this question we are given a circuit in the figure and we want to write the three loop equations based on kerchops rule for the different loops.

00:13 So one of the main things to note is that when we are following the loop, when we bypass a battery, if you are moving from the minus to the plus end, we will add our potential.

00:31 But if you are moving from the plus to the minus m, we'll subtract the potential.

00:38 Next, if you are bypassing a resistor, if a current is in this direction and we are following the same direction as the current, then we will subtract away the potential drop across this resistor, that is ir.

01:00 But if we are moving against the current then we will add the potential drop which is plus i so this is all the all the considerations that we'll need so let us start with loop 1 so for loop 1 we start off with the battery we are moving from minus to positive so we will add our potential that's v1 then we bypass r2 in the same direction as the current so we'll subtract away the potential drop i2 r2 next we are bypassing r1 right in the same direction as the current and we know that because at the junction where there is i2 and i4 coming in we know that from kerchhoff's junction this the left wire must have a current that is flowing out of the junction because you can't have all of the current flowing inwards into a junction right you will not get a net current of zero for that particular junction which you need so the current must be flowing to the left and hence the loop is in the same direction as our current and so we would subtract away the potential drop.

02:45 So we're assuming that the current over here will be equals to i1, make the same current that is flowing outwards from the battery.

03:00 There'll be i1r1.

03:03 We create this to zero because by kerchov's rule we know the entire loop must have a total of zero potential right after adding all of them.

03:16 So this is our first equation.

03:18 So now we move on to the second loop using the same idea.

03:23 We start off at the battery again, v2.

03:27 Now for this time we are moving from positive to negative n of the battery.

03:32 So we have to subtract v2...