(a) Find the equivalent resistance between points A and B for the combination of resistors shown

(a) Find the equivalent resistance between points A and B...

Key Concepts

Equivalent Resistance

Equivalent resistance is the total resistance that a circuit presents to an external source when multiple resistors are combined. By reducing a network of resistors into a single resistor using series and parallel combinations, it simplifies calculations of circuit behavior such as current flow and voltage distribution.

Series Resistor Combination

In a series resistor combination, resistors are arranged end-to-end so that the same current flows sequentially through each. The total resistance is simply the sum of the individual resistances. This configuration causes the applied voltage to be divided among the resistors proportionally to their resistances.

Parallel Resistor Combination

In a parallel resistor combination, resistors are connected across the same two points so that the voltage across each resistor is identical. Instead of adding directly, the reciprocals of the resistances are summed to find the reciprocal of the equivalent resistance, which results in a lower total resistance than any individual resistor in the parallel network.

Ohm's Law

Ohm's Law is a fundamental relation in circuit analysis which states that the voltage (V) across a resistor is directly proportional to the current (I) flowing through it and the resistance (R) of the resistor, expressed as V = IR. This principle is essential for analyzing and solving electrical circuits.

Voltage Division

The voltage division principle explains how the total voltage in a series circuit is divided among the resistors based on their resistance values. Each resistor in series drops a portion of the total voltage proportional to its resistance, making it straightforward to calculate the voltage across any individual resistor in the chain.

Current Division

The current division principle applies to parallel circuits and describes how the total current entering a junction splits among the parallel branches. The current in each branch is inversely proportional to the branch’s resistance, allowing the calculation of the current through any specific resistor in the parallel network.

Transcript

00:01 Hi, in the given problem here this is a circuit diagram having a combination of various resistors.

00:12 The first one is 2 .0 om, then here this is 1 .0, another 1 .0 om in series with it, then 2 4 ome resistors in parallel with each other.

00:45 And then finally, a 3 .0 -oam resistor.

00:55 Then across all of them, a 6 .0 -home resistor, and then a battery, providing a potential of 12 .0 volt.

01:11 Now, in the first part of the problem, we have to find equivalent resistance between the terminals a and b.

01:23 First of all, these 2 4 -oom resistors are in a parallel combination.

01:32 So their net resistance will be denoted by r subscript p.

01:38 Then these 2 1 -oom resistors are in series.

01:45 So we will represent their net combination as r s.

01:50 So using the rule of parallel combination here this rp will be given by 4 .0 by 2 ome means this is 2 .0 and this series combination r s is 1 .0 plus 1 .0 ome means this is 2 .0 om.

02:14 Now this r p and r s are in parallel combination so, the net resistance may be represented as rp dash that will be given by 2 .0 divided by 2.

02:41 As we know, when identical resistors are put in parallel combination, then net resistance of parallel combination is given by the value of one resistor divided by the number of resistors.

02:55 Here the two resistors, rp and rs both are having 2 .0 om and these are two in number.

03:01 That's why this is 1 .0 om.

03:05 Finally, this rp dash complete here, this is rp dash complete.

03:17 This is in series with 2 .0 om and 3 .0 om.

03:21 So, as r p dash 2 .0 om and 3 .0 om are in series.

03:35 So the net resistance which may be represented as r s dash is given as 2 .0 plus 1 .0 for rp dash plus 3 .0 ome which comes out to be 6 .0...

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