# SIMPLIFICATION OF RESISTIVE CIRCUITS

What is circuit simplification?

The simplification of resistive electrical circuits helps us to interpret the ohm law much more easily since to apply the current formula for a circuit we need to know the value of the resistance and the voltage of the circuit.

But what happens when we have more than one resistance?

When we have more than one value, the whole process is difficult, since this formula is only designed to calculate the current with only one resistance and one voltage data. This is where the simplification of the circuits comes in. To obtain the total resistance we have to reduce the circuit until we are left with only the basic circuit that would be, a voltage source and a resistor.

electrical circuit

Types of resistive circuits

There are three ways to group the circuits: In series, in parallel and mixed. The latter is the combination of the first two.

Series circuits

This type of circuit is generated when the resistors are connected only by one terminal (one behind the other). The main characteristic of these circuits is that the current is always the same throughout the circuit and the voltage decreases with each resistance. the formula to calculate these circuits is the sum of each one RT = R1 + R2 + R3 +… + Rn

series circuit

Parallel circuits

The resistors are connected in the same way, terminal 1 with 1 and 2 with 2. The current and voltage within these circuits work in reverse since the voltage that passes through each element is the same, but the current decreases with each resistor. There are 2 formulas for these circuits when there are only 2 devices in parallel RT = R1 * R2 / R1 + R2 and when there are more than two RT = 1 / (1 / R1 + 1 / R2 + 1 / R3 +… + 1 / Rn ).

parallel circuit

Mixed circuits

These circuits are more complex because we can find resistors in series and in parallel. To simplify this circuit, you have to identify which parts can be solved first and how they are.

mixed circuit

Examples

Series circuit

This type of circuit is the simplest since only the resistance values are added together. the only thing we have to take care of is when we have KΩ and Ω since 1KΩ = 1,000Ω.

simplification of circuits

Parallel circuit

When it is a purely parallel circuit it does not have much difficulty since we only use a formula, even though we always have to be attentive to the values of the resistances.

Simplification of circuits

Mixed circuit

For the simplification of mixed circuits the difficulty can increase or decrease, since depending on the circuit some may be more elaborate and complex and some others may be quite simple. Remember to observe the resistance values well at all times.

circuit simplification

Once the first steps have been resolved, the results are replaced to continue looking for possible progress until reaching maximum simplification. R1,2 – R7,6 and R4,5 are handled in this way to know that the result came from the simplification of R1 and R2 or as the case may be.

Mixed circuit

Finally, we will be able to realize that all the excess resistances were left in series, it is only enough to apply the formula to and we managed to find the total resistance of the circuit.

Simplification of circuits

Once removing the total resistance and the current that circulates through the circuit we can extract the voltage of each resistance, the current that circulates in each mesh, etc. (soon article on that topic