Electrical Engineering: Basic Laws (17 of 31) Finding the Equivalent Resistor Ex. 2

Summary

This video explains how to calculate the equivalent resistance of a complex resistor circuit step by step. Starting with resistors in series and parallel, it demonstrates how to simplify the circuit by combining resistors in series first and then parallel. The example uses identical resistors, emphasizing how to identify which resistors are in series or parallel based on shared nodes. The process culminates in finding the total equivalent resistance using the product-over-sum formula for parallel resistors and adding resistances in series. The explanation highlights how these methods apply to circuit analysis.

Takeaways

• 🔗 All the resistors in the circuit have the same value.
• 🔧 The analysis starts from the far end of the circuit, specifically between terminals A and B.
• 🌀 The first three resistors are in series because they share a common node exclusively.
• ➕ The total resistance of resistors in series is the sum of their individual resistances.
• 🧮 In the first case, three resistors are combined into a single equivalent resistor with a value of 3R.
• 🔀 Next, two resistors are identified to be in parallel because they share common nodes on both ends.
• 📉 The equivalent resistance of two parallel resistors is calculated using the product-over-sum formula.
• ➗ The parallel combination results in an equivalent resistance of 6/5R.
• 🔄 The circuit is then redrawn, simplifying it with the new equivalent resistances.
• 💡 Finally, the remaining resistors in the simplified circuit are in series, leading to a final total resistance of 3 + 1/5R.

Q & A

What is the main goal of analyzing the circuit in the script?

The main goal is to find the equivalent resistance of the circuit by simplifying the resistors, which are arranged in series and parallel combinations.

How do we know the resistors are in series at the beginning of the circuit analysis?

The resistors are in series because they share a common node exclusively, meaning the current flows through each resistor one after another without branching.

What is the equivalent resistance of three resistors in series, each with a resistance of R?

The equivalent resistance of three resistors in series is the sum of their resistances, which is 3R (R + R + R).

How do we determine if two resistors are in parallel?

Two resistors are in parallel if they share the same nodes on both ends, allowing current to split between them.

What is the formula for calculating the equivalent resistance of two resistors in parallel?

The equivalent resistance of two resistors in parallel is given by the formula: R_total = (R1 * R2) / (R1 + R2).

How is the equivalent resistance of the two parallel resistors calculated in the script?

The equivalent resistance is calculated as (2R * 3R) / (2R + 3R), which simplifies to 6R^2 / 5R, resulting in 6/5R.

Why is the equivalent resistance of two resistors in parallel always smaller than the smallest resistor?

In parallel, the total resistance decreases because the current has more paths to flow through, making the combined resistance lower than the smallest individual resistor.

After calculating the parallel combination, how does the circuit look when redrawn?

The circuit is redrawn with a 6/5R resistor in place of the two parallel resistors and two other resistors with values R and R in series.

How do you find the total equivalent resistance of the final series circuit?

The total equivalent resistance is found by adding the three resistors in series: R + 6/5R + R, which equals 3 + 1/5R or 16/5R.

What is the significance of simplifying circuits by finding equivalent resistances?

Simplifying circuits helps in easier analysis and calculation of important electrical properties like current, voltage, and power, as it reduces complex circuits into simpler forms.