# How Do You Calculate the Equivalent Resistance in This Circuit?

• rootX
In summary, the conversation involves finding the equivalent resistance in a circuit shown in an image. The attempt at a solution involves using the equation R_eq^-1 = (30+60)^-1+(40+10)^-1, but the accuracy of the answer is being questioned. The suggestion is made to check the answer using the equation R_{eq} = \frac{R_1 \cdot R_2}{R_1 + R_2}, with R1 being 90 and R2 being 50.
rootX

## Homework Statement

Find equivalent resistance in:
http://img135.imageshack.us/img135/585/62083770ay3.jpg

## The Attempt at a Solution

my
r_eq^-1 = (30+60)^-1+(40+10)^-1
this is wrong.
do i need to include 8 and 4 ohm resistors

Last edited by a moderator:
rootX said:

## Homework Statement

Find equivalent resistance in:
http://img135.imageshack.us/img135/585/62083770ay3.jpg

## The Attempt at a Solution

my
r_eq^-1 = (30+60)^-1+(40+10)^-1
this is wrong.
do i need to include 8 and 4 ohm resistors

Based on your drawing your equation looks correct. What answer did you get?

You can check your answer against this equation's results:

$$R_{eq} = \frac{R_1 \cdot R_2}{R_1 + R_2}$$

R1 would be 90 since 30 and 60 are in series and R2 would be 50 for the same reason.

CS

Last edited by a moderator:
in the calculation?

I would first like to clarify that the concept of equivalent resistance refers to the total resistance in a circuit that is equivalent to the original circuit. This is useful in simplifying complex circuits and understanding the overall behavior of the circuit.

In order to find the equivalent resistance in this circuit, we can use the formula R_eq = R_1 + R_2 + ... + R_n, where R_1, R_2, etc. are the individual resistances in the circuit.

Based on the given circuit, we can see that the 30 ohm and 60 ohm resistors are in parallel, as well as the 40 ohm and 10 ohm resistors. Therefore, we can use the formula for equivalent resistance in parallel circuits, which is R_eq = (R_1 * R_2)/(R_1 + R_2).

Applying this formula, we get an equivalent resistance of 18 ohms for the parallel combination of 30 ohm and 60 ohm resistors, and an equivalent resistance of 8 ohms for the parallel combination of 40 ohm and 10 ohm resistors.

Now, we can see that the 18 ohm and 8 ohm resistors are in series, so we can simply add them together to get a final equivalent resistance of 26 ohms for the entire circuit. Therefore, the answer to the given problem is 26 ohms.

To answer your question, yes, you do need to include the 8 ohm and 4 ohm resistors in the calculation as they are part of the circuit and contribute to the overall resistance.

I hope this explanation helps. Keep up the good work in your studies of circuits and resistances!

## 1. What is equivalent resistance?

Equivalent resistance refers to the combined resistance of multiple resistors in a circuit. It represents the overall resistance that a single resistor would need to have in order to produce the same effect as the combination of resistors in the circuit.

## 2. How is equivalent resistance calculated?

Equivalent resistance is calculated using Ohm's law, which states that resistance is equal to voltage divided by current. For resistors in series, the equivalent resistance is the sum of all individual resistances. For resistors in parallel, the equivalent resistance is equal to the reciprocal of the sum of the reciprocals of each individual resistance.

## 3. Why is equivalent resistance important?

Equivalent resistance is important because it helps us understand the overall behavior of a circuit. It allows us to simplify complex circuits and analyze them more easily. It also helps in determining the amount of current and voltage in a circuit.

## 4. What happens to equivalent resistance when resistors are added in series or parallel?

The equivalent resistance increases when resistors are added in series, as the overall path for current becomes longer. On the other hand, the equivalent resistance decreases when resistors are added in parallel, as there are multiple paths for current to flow through.

## 5. Can equivalent resistance ever be lower than the lowest individual resistance?

No, the equivalent resistance can never be lower than the lowest individual resistance, regardless of whether the resistors are in series or parallel. This is because adding more resistors can only increase the overall resistance, not decrease it.

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