Parallel connection of resistors, along with serial, is the main way to connect elements in an electrical circuit. In the second embodiment, all elements are installed in series: 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. Conditionally for direct current, we can designate them as plus and minus, and for alternating 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 direct and alternating current.
Calculation of the total resistance with parallel connection of resistors
Unlike a series connection, where to find the total resistance it is enough to add the value of each element, for parallel the same will be true for conductivity. And since it is inversely proportional to resistance, we obtain the formula presented together with the circuit in the following figure:
One important feature of calculating the parallel connection of resistors should be noted: the total value will always be less than the smallest of them. For resistors, it 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 the voltage and current strength. In this case, Ohm's law, which determines the relationship between resistance, current strength and voltage, will help us.
Based on the first formulation of the Kirchhoff law, we find that the sum of the currents converging in one node is equal to zero. The direction is chosen in the direction of current flow. Thus, the incoming current from the power source can be considered a positive direction for the first node. And negative will be outgoing from each resistor. For the second node, the picture is opposite. Based on the wording of the law, we find 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 law of Kirchhoff. It is the same for each resistor and is equal to the total. This feature is used to connect outlets and lighting in apartments.
Calculation Example
As a first example, we give the calculation of resistance in parallel connection of identical resistors. The current flowing through them will be the same. An example of calculating the resistance looks like this:
In this example, it is clearly seen that the total resistance is two times lower than each of them. This corresponds to the fact that the total current strength is two times higher than that of one. It also correlates well with a twofold increase in conductivity.
Second example
Consider an example of parallel connection of three resistors. For the calculation we use the standard formula:
In a similar way, circuits with a large number of parallel connected resistors are calculated.
Mixed compound example
For a mixed compound, for example, presented below, the calculation will be carried out in several stages.
To begin with, successive elements can be arbitrarily replaced with one resistor with a resistance equal to the sum of two replaced. Further, we consider the total resistance in the same way as for the previous example. This method is also suitable for other more complex schemes. By sequentially simplifying the scheme, you can get the necessary value.
For example, if instead of resistor R3 two parallel ones are connected, you will first need to calculate their resistance, replacing them with an equivalent one. And then the same as in the example above.
Applying a parallel circuit
The parallel connection of resistors finds its application in many cases. Serial connection increases the resistance, but for our case it will decrease. For example, an electrical circuit requires a resistance of 5 ohms, but there are only resistors of 10 ohms or more. From the first example, we know that you can get half the resistance value if you install two identical resistors parallel to each other.
The resistance can be reduced even more, for example, if two pairs of parallel-connected resistors are connected in parallel with respect to each other. You can reduce the resistance by half if the resistors have the same resistance. By combining with a serial connection, you can get any value.
The second example is the use of a 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 using a parallel connection is the protective grounding of electrical equipment. For example, if a person touches the metal case of the device, on which the breakdown will occur, a parallel connection will be obtained between it and the protective conductor. The first node will be the place of contact, and the second zero point of the transformer. 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 larger. If there were no grounding, all the current flowing in the circuit would go through a person, since he would be the only conductor.
Parallel connection can also be used for batteries. The voltage remains the same, but their capacity doubles.
Total
When connecting resistors in parallel, the voltage across them will be the same, and the current is equal to the sum flowing through each resistor. Conductivity will equal the sum of each. From this, an unusual formula for the total resistance of the resistors is obtained.
It is necessary to take into account when calculating the parallel connection of resistors that the resulting resistance will always be less than the smallest. This can also be explained by summing the conductivity of the resistors. The latter will increase with the addition of new elements, respectively, and the conductivity will decrease.