How to perform parallel connection of resistors?

In order to regulate the magnitude of the current and voltage in the circuit, a special connection of the resistors is made. Sequentially connected elements limit the current in the circuit, and parallel connected create an additional voltage drop, thereby limiting the magnitude of the potential difference to consumers that are in the same circuit.

You can use one resistor of the desired value, but it is not always possible to make the necessary calculations to determine the optimum value. Therefore, it is more expedient to select resistance by combining different quantities.

Parallel connection of resistors is made by connecting the beginnings and ends of all elements to one node. Thus, a scheme is obtained, where, depending on the value of each element, a total voltage drop of the entire circuit is created.
The total resistance of the resistors connected in parallel is calculated by a special formula.

It should be remembered that if parallel connection of resistors is made, then the total resistance of all elements will be unambiguously smaller than the smallest resistance entering into the circuit.

However, there are several special cases that can not be forgotten. If only two resistors are included in the circuit, then their total resistance is calculated as the difference between their product and the sum: Rmain = R1R2 / R1 + R2.

The next special case is a connection in which many resistors with the same resistance value are included. In this case, the total value is defined as the difference of the value of one resistance by the number of elements, that is: Rmain = R1 / n.

Since the parallel connection of the resistors is two nodes, it is obvious that the difference in their potentials is the same as the potential difference between the two nodes. Thus, it is reasonable to conclude that the voltages on each of the elements are equal to each other. It looks like this: U = U1 + U2 + U3 + .... + Un.

If both nodes forming a parallel connection of the resistors are directly connected to the power supply terminals , then the voltage of each of the resistors will be equal to the voltage generated by the source itself: U1 + U2 + U3 + .... + Un = U.

Another feature of the connection of resistances in the scheme of parallel inclusion is the electric current. It is distributed by branches in inverse proportion to the resistances of these sections. In other words: the greater the resistance, the lower the current, and vice versa, the larger the current, the lower the resistance. This is Ohm's first law: I = U / R.

The total current in the node will be equal to the sum of the current in each branch separately. After all, charges can not accumulate at nodes, so the first Kirchhoff law should be noted , which reads: "The sum of the currents that enter the node is equal to the sum of the currents that come out of it." It can be said more simply that the sum of the currents at the node is zero. And the expression is written like this: "The sum of the currents is zero."

The laws presented here are relevant for circuits without inductance and capacitance. If the parallel connection of the resistors is in the same circuit as the coil or capacitor, then it is necessary to find the impedance taking into account all the elements. For this, inductive and capacitive resistances are calculated.