# Find the equivalent resistance in a circuit

• jakobsandberg
In summary, the equivalent resistance in the circuit is 4 Ohms, with the two 4 Ohm resistors in series and two 8 Ohm resistors in parallel. This can be confirmed using Kirchhoff's law.
jakobsandberg

## Homework Statement

Find the equivalent resistance in the circuit below:

## The Attempt at a Solution

I know the two 4 Ohm resistors (on the same wire) are in series and thus add to 8 Ohms. However, I do not know where to go from here. When the resistors are in a box, with one on each side, are they in series? Or are they two parallels?

Thanks!

I believe the 2,4,2 ohm resistors are all in series since the same current flows through them.

rock.freak667 said:
I believe the 2,4,2 ohm resistors are all in series since the same current flows through them.

So this would leave me with two parallel resistors of 8 Ohms each? And finding the equivalent resistance would give us 4 Ohms?

If you (or someone else) can confirm this, it would be greatly appreciated!

yep. 8 ohm 8ohm are in parrellel giving 4 ohm net resistance. can be veryfied using kirhoff's law to show current in both branches are the same.

To find the equivalent resistance in this circuit, we can use the following formula:

Req = R1 + R2 + R3 + ...

In this case, we have two 4 Ohm resistors in series, so we can add them together to get 8 Ohms. Then, we have two more resistors in parallel, which means that their equivalent resistance is given by:

Req = (1/R4 + 1/R5)^-1

Plugging in the values, we get:

Req = (1/6 + 1/6)^-1 = 3 Ohms

Therefore, the equivalent resistance in this circuit is 8 Ohms + 3 Ohms = 11 Ohms. Remember to always consider the arrangement of resistors (parallel or series) when calculating the equivalent resistance. In this case, the two resistors on each side of the box are in parallel, while the two 4 Ohm resistors are in series. I hope this helps!

## 1. How do you find the equivalent resistance in a circuit?

To find the equivalent resistance in a circuit, you can use the formula Req = R1 + R2 + ... + Rn, where R1 to Rn are the individual resistances in the circuit. You can also use a combination of series and parallel resistor equations to find the equivalent resistance.

## 2. Why is it important to find the equivalent resistance in a circuit?

It is important to find the equivalent resistance in a circuit because it allows you to determine the total resistance in the circuit. This information is crucial in calculating the current and voltage in the circuit, which are important in understanding the overall behavior of the circuit.

## 3. What is the difference between series and parallel resistors?

In series resistors, the resistances are connected end to end, creating a single pathway for the current to flow through. In parallel resistors, the resistances are connected side by side, creating multiple pathways for the current to flow through. This results in different equations to calculate the equivalent resistance.

## 4. Can the equivalent resistance be less than the individual resistances in a circuit?

Yes, the equivalent resistance can be less than the individual resistances in a circuit. This happens when the resistors are connected in parallel, as the total resistance decreases when more pathways are created for the current to flow through.

## 5. Are there any limitations to finding the equivalent resistance in a circuit?

There are some limitations to finding the equivalent resistance in a circuit. This method assumes that the resistors are all linear and do not have any complex properties. It also does not take into account any temperature changes that may affect the resistances. Additionally, the equivalent resistance only applies to DC circuits and not AC circuits.

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