Find the equivalent resistance between points A and B in the...

Key Concepts

Equivalent Resistance

Equivalent resistance is a simplified single resistance that can replace a complex network of resistors to yield the same overall electrical behavior between two points in a circuit. This concept is crucial for analyzing and understanding the distribution of current and voltage in a circuit.

Resistors in Series

Resistors in series are connected end-to-end, so the same current flows through each resistor. The total or equivalent resistance in a series configuration is the sum of the individual resistances, as each resistor adds to the total opposition to current flow.

Resistors in Parallel

Resistors in parallel are connected such that the voltage across each resistor is the same. The equivalent resistance is found by taking the reciprocal of the sum of the reciprocals of each individual resistance, which generally results in a total resistance that is lower than any individual resistor's resistance.

Circuit Analysis

Circuit analysis involves the use of various methods and techniques to simplify and solve electrical networks. This includes identifying series and parallel components, applying rules such as Kirchhoff’s laws, and sometimes employing transformations to reduce complex circuits into simpler forms for easier calculation of parameters such as equivalent resistance.

Transcript

00:01 So in this problem, we have seven different registers combined, and we want to find out the total resistance at point a, b.

00:11 So what i'm going to do i'm doing here is i'm labeling all of these registers, r1, r2, r3, r4, r5, r6, and r7.

00:22 I just labeled it this way, but you can label them however you want.

00:26 All right.

00:26 Now, first of all, look at where you can start, all right? so you can see that r1, r2, and r3 are in series.

00:38 Okay, so let's just start from here.

00:41 All right.

00:42 So that means r1, 2, 3 equals r1 plus r2 plus r3, and that is going to be 1 plus 2 plus 3 which is going to be equal to 6 om okay now i'm going to simplify the circuit the simplified circuit is going to look like this so now this guy over here is r1 2 3 and this guy over here is r4 and we have another one guy here r6, so this is how the simplified circuit looks like.

01:36 R7, r6, r5, r4, and this guy here is 1, 2, 3.

01:48 Now if you look at this figure, you can see that r1 ,2 ,3 is in parallel with r4.

01:55 So the total resistance in this case is going to be r1, 2, 3, 4 is going to be equal to r1, 2, 3 parallel r4.

02:11 So that's going to be r1, 2, 3 times r4 over r1, 2, 3 plus r4.

02:24 And this is going to be equal to 6 oh never mind that's not going to be equal to 6 o this is going to be equal to 2 all all right and the new simplified circuit is going to look like this over here so this is r7 this is going to be r5 and this is going to be r 1 2 3 4 and this is going to be r so now this is point a, b, r7, r6, r5, r1, 2, 3, 4...

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