# Solve Circuit for R(ab): Equivalent Resistance 20 Ohms?

• Engineering
• jonathan.15
In summary, the question asks to find the Equivalent resistance R(ab) for the circuit. While it may seem like an open circuit with infinite resistance between points A and B, the answer in the book is 20 ohms. This is because the current can flow through the circuit by picking off pairs of resistors in series and parallel, ultimately reducing the circuit to just one resistor connecting A and B. This may initially seem counterintuitive, but after reducing the circuit it becomes clear that the resistance is indeed 20 ohms.
jonathan.15

The question asks to find the Equivalent resistance R(ab) for the circuit. Is this a trick question? Because I thought it is an open circuit and therefore the resistance between a and b would be infinite. The answer in the book is 20 ohms, please explain if possible

Why do you think the resistance is infinite? There are lots of ways the current can flow from a to b.

You can solve this by picking off pairs of resistors that are in series and parallel, and replacing then with a single resistor. You will end up with just one resistor connecting a and b.

Because there is no wire connecting points A and B I thought this is an open circuit, which has infinite resistance?

This is my final step in reducing the circuit, so now this makes sense that the resistance would be 20, I kept thinking that current would not flow flow from a down to b because they were separated but they are connected

Moderator's note: thread moved from Electrical Engineering.

## 1. What is circuit resistance and why is it important?

Circuit resistance refers to the overall opposition to the flow of electrical current in a circuit. It is important because it affects the amount of current that can flow through a circuit, which in turn affects the performance of the circuit.

## 2. How do I calculate equivalent resistance in a circuit?

To calculate equivalent resistance in a circuit, you need to use Ohm's Law, which states that resistance is equal to voltage divided by current. You will also need to use the formula for calculating resistors in series or in parallel, depending on the circuit configuration. Once you have calculated the individual resistances, you can add them together to get the equivalent resistance.

## 3. What is the significance of a 20 Ohm equivalent resistance?

A 20 Ohm equivalent resistance means that the overall opposition to the flow of current in the circuit is equal to 20 Ohms. This value can help determine the performance of the circuit and what components may need to be added or adjusted to optimize its function.

## 4. How do I use equivalent resistance in circuit analysis?

Equivalent resistance is used in circuit analysis to simplify complex circuits and make it easier to calculate current, voltage, and power. By replacing multiple resistors with a single equivalent resistance, the circuit can be reduced to a simpler form, making it easier to analyze and understand.

## 5. Can equivalent resistance ever be lower than the smallest resistor in a circuit?

No, equivalent resistance can never be lower than the smallest resistor in a circuit. This is because adding more resistors in parallel will decrease the overall resistance, but never to a value lower than the smallest resistor present. This is known as the rule of reciprocal resistances.

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