For a series circuit, the formula for total resistance is:

We are given the values of each resistance, allowing us to sum them to find the total resistance in the circuit.

The formula for resistance in parallel is:

We are given the values for each individual resistor, allowing us to solve for the total resistance.

The resistance of a wire is given by the following equation:

We are given the resistivity (), cross-sectional area, and length. Using these values, we can solve for the resistance.

First, convert the cross-sectional area to square-meters.

Use the resistance equation to solve.

The formula for resistors in series is .

Plug in our given values.

The equation for resistors in parallel is:

We are given the values of the resistors. Using this formula, we can solve for the equivalent resistance.

Plug in the given values and solve.

For resistors aligned in series, the equivalent resistance is the sum of the individual resistances.

Since all the resistors in this problem are equal, we can simplify with multiplication.

The formula for resistance in parallel is:

We are given the values for each individual resistor, allowing us to solve for the total resistance.

Think of resistors as doors, preventing the flow of people (electrons). Imagine the following scenarios: a large group of people are in a room and all try to leave at once. If the five resistors are in series, that's like having all of these people trying to go through all five doors before they can leave. In a circuit, all the electrons in the current mast pass through every resistor.

If the resistors are in parallel, it's like having five separate doors from the room. All of a sudden, the group can leave MUCH faster, encountering less resistance to their flow out of the room. The path of the electrons can split, allowing each particle to pass through only one resistor.

From a formula perspective, the resistors in series are simply summed together to find the equivalent resistance.

In parallel, however, the reciprocals are summed to find the reciprocal equivalent resistance.

Adding whole numbers will always give you a much greater result than adding fractions. For the exact same set of resistors, arrangement in series will have a greater total resistance than arrangement in parallel.

In basic resistors, energy lost due to resistance is converted into heat. In some cases, other conversions also take place (such as generation of light in a lightbulb), but heat is still dissipated along with any alternative conversations. Lightbulbs, batteries, and other types of resistors will become hot as current passes through them.

The formula for resistance is: 

Above,  is length,  is the cross-sectional area of the wire, and  is the resistivity of the material, and is a property of that material. The resistivity is constant for a given material, and thus cannot be changed by altering the dimensions of the wire.