# Electric Circuits (resolving them)

• bobnojio
In summary, there is more than one way to connect four identical resistors together to achieve an equivalent resistance of R. Some possible combinations include two series combinations in parallel, two parallel combinations in series, and the circuit mentioned in the previous response. However, it is not possible to have any of the resistors be 'open circuited' in order to achieve the desired resistance.
bobnojio
"you have four identical resistors, each with a resistance of R. You are asked to connect these four together so that the equivalent resistance of the resulting combination is R, How many ways can you do it? There is more than one way. Justify your answer"

I can only think of ONE way to do this. (you can neglect a voltage or current source, as its equivalent resistors), but for good measure, let V be the voltage source, ignore the .'s

|----|----|
|...|...|
V...R...R
|...|...|
|...R...R
|----|----|

Can anyone help me find any other combinations of these four identical resistors that gives the same resistance as the equivalent?

as far as I know, i am not allowed to have any of the resistors being 'open circuited' so that they do not affect the circuit.

any help is greatly appreciated

Last edited:
bobnojio said:
"you have four identical resistors, each with a resistance of R. You are asked to connect these four together so that the equivalent resistance of the resulting combination is R, How many ways can you do it? There is more than one way. Justify your answer"

I can only think of ONE way to do this. (you can neglect a voltage or current source, as its equivalent resistors), but for good measure, let V be the voltage source, ignore the .'s

|----|----|
|...|...|
V...R...R
|...|...|
|...R...R
|----|----|

Can anyone help me find any other combinations of these four identical resistors that gives the same resistance as the equivalent?

as far as I know, i am not allowed to have any of the resistors being 'open circuited' so that they do not affect the circuit.

any help is greatly appreciated

I suppose it depends on what constitutes a unique circuit. For instance you can put in series two parallel combinations. Equivalently you can put in parallel two series combinations.

There are actually multiple ways to connect four identical resistors together to achieve an equivalent resistance of R. Here are a few examples:

1. Series Connection: In this arrangement, all four resistors are connected in a straight line, with one end of the first resistor connected to one end of the second resistor, and so on. The equivalent resistance in this case would be R + R + R + R = 4R.

2. Parallel Connection: In this arrangement, all four resistors are connected side by side, with one end of each resistor connected to one end of the others. The equivalent resistance in this case would be 1/(1/R + 1/R + 1/R + 1/R) = R/4.

3. Combination of Series and Parallel Connection: In this arrangement, two resistors are connected in series, and then this combination is connected in parallel with another two resistors connected in series. The equivalent resistance in this case would be (R + R) || (R + R) = (2R)(2R)/(2R + 2R) = R.

There are also other possible combinations, such as connecting all four resistors in a diamond shape, or connecting three resistors in series and one in parallel, etc. The key is to understand the concept of series and parallel connections and use them in different combinations to achieve the desired equivalent resistance.

## 1. What is an electric circuit?

An electric circuit is a path that allows electric current to flow. It is made up of various components such as a power source, conductors, and loads, which work together to create a complete circuit.

## 2. How do you resolve a series circuit?

To resolve a series circuit, you can use Kirchhoff's voltage law and Ohm's law. Kirchhoff's law states that the sum of voltage drops in a closed loop must be equal to the applied voltage. Ohm's law states that the current in a circuit is directly proportional to the voltage and inversely proportional to the resistance.

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

In a series circuit, the components are connected in a single loop, whereas in a parallel circuit, the components are connected in multiple branches. In a series circuit, the current is the same throughout, while in a parallel circuit, the voltage is the same throughout.

## 4. How do you calculate the total resistance in a parallel circuit?

To calculate the total resistance in a parallel circuit, you can use the formula 1/Rt = 1/R1 + 1/R2 + 1/R3... where Rt is the total resistance and R1, R2, R3... are the resistances of each branch. You can also use the reciprocal method, where you add the reciprocals of each resistance and take the reciprocal of the sum.

## 5. What is the purpose of a circuit breaker?

A circuit breaker is a safety device that is used to protect an electric circuit from overload or short circuit. It automatically interrupts the flow of electricity when it detects a fault, preventing damage to the circuit and potential hazards such as electrical fires.

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