Parallel connection of resistors, along with series, is the main way to connect elements in an electrical circuit. In the second version, all elements are installed sequentially: the end of one element is connected to the beginning of the next. In such a circuit, the current strength on all elements is the same, and the voltage drop depends on the resistance of each element. There are two nodes in a serial connection. The beginnings of all elements are connected to one, and their ends to the second. Conventionally, for direct current, you can designate them as plus and minus, and for alternating current as phase and zero. Due to its features, it is widely used in electrical circuits, including those with a mixed connection. The properties are the same for DC and AC.
Calculation of total resistance when resistors are connected in parallel
Unlike a series connection, where to find the total resistance it is enough to add the value of each element, for a parallel connection, the same will be true for conductivity. And since it is inversely proportional to the resistance, we get the formula presented along with the circuit in the following figure:
It is necessary to note one important feature of the calculation of the parallel connection of resistors: the total value will always be less than the smallest of them. For resistors, this is true for both direct and alternating current. Coils and capacitors have their own characteristics.
Current and voltage
When calculating the parallel resistance of resistors, you need to know how to calculate voltage and current. In this case, Ohm's law will help us, which determines the relationship between resistance, current and voltage.
Based on the first formulation of Kirchhoff's law, we obtain that the sum of the currents converging in one node is equal to zero. The direction is chosen according to the direction of current flow. Thus, the positive direction for the first node can be considered the incoming current from the power supply. And the outgoing from each resistor will be negative. For the second node, the picture is opposite. Based on the formulation of the law, we get that the total current is equal to the sum of the currents passing through each resistor connected in parallel.
The final voltage is determined by the second Kirchhoff law. It is the same for each resistor and is equal to the total. This feature is used to connect sockets and lighting in apartments.
Calculation example
As the first example, let's calculate the resistance when connecting identical resistors in parallel. The current flowing through them will be the same. An example of calculating resistance looks like this:
This example clearly shows thatthat the total resistance is twice as low as each of them. This corresponds to the fact that the total current strength is twice as high as that of one. It also correlates well with doubling the conductivity.
Second example
Consider an example of a parallel connection of three resistors. To calculate, we use the standard formula:
Similarly, circuits with a large number of resistors connected in parallel are calculated.
Mixed connection example
For a mixed compound such as the one below, the calculation will be done in several steps.
To begin with, serial elements can be conditionally replaced by one resistor with a resistance equal to the sum of the two replaced. Further, the total resistance is considered in the same way as for the previous example. This method is also suitable for other more complex schemes. Consistently simplifying the circuit, you can get the desired value.
For example, if two parallel resistors are connected instead of R3, you will first need to calculate their resistance, replacing them with an equivalent one. And then the same as in the example above.
Application of a parallel circuit
Parallel connection of resistors finds its application in many cases. Connecting in series increases the resistance, but in our case it will decrease. For example, an electrical circuit requires a resistance of 5 ohms, but there are only 10 ohm and higher resistors. From the first example, we knowthat you can get half the resistance value if you install two identical resistors in parallel with each other.
You can reduce the resistance even more, for example, if two pairs of resistors connected in parallel are connected in parallel relative to each other. You can reduce the resistance by a factor of two if the resistors have the same resistance. By combining with a serial connection, any value can be obtained.
The second example is the use of parallel connection for lighting and sockets in apartments. Thanks to this connection, the voltage on each element will not depend on their number and will be the same.
Another example of the use of parallel connection is the protective earthing of electrical equipment. For example, if a person touches the metal case of the device, on which a breakdown occurs, a parallel connection will be obtained between it and the protective conductor. The first node will be the place of contact, and the second will be the zero point of the transformer. A different current will flow through the conductor and the person. The resistance value of the latter is taken as 1000 ohms, although the real value is often much higher. If there were no ground, all the current flowing in the circuit would go through the person, since he would be the only conductor.
Parallel connection can also be used for batteries. The voltage remains the same, but their capacitance doubles.
Result
When resistors are connected in parallel, the voltage across them will be the same, and the currentis equal to the sum of the currents flowing through each resistor. Conductivity will equal the sum of each. From this, an unusual formula for the total resistance of resistors is obtained.
It is necessary to take into account when calculating the parallel connection of resistors that the final resistance will always be less than the smallest. This can also be explained by the summation of the conductance of the resistors. The latter will increase with the addition of new elements, and, accordingly, the conductivity will decrease.
