Resistance in parallel formula calculation

In practice often occurs the problem of finding the resistance of conductors and resistors at various ways of connection. The article considers how to calculate resistance in a parallel connection of conductors and some other technical issues.

Conductor Resistance

All conductors tend to hinder the flow of electric current, it is called electric resistance R, it is measured in ohms. This is the main property of electrically conductive materials.

For doing calculations of the electrical resistivity is applied – ρ Om·m/mm². All metals-good conductors, the most used were copper and aluminium, is much less used iron. The best conductor-silver, it is used in electrical and electronic industry. Widespread alloys with a high resistance value.

In the calculation of the resistance used well-known from school physics formula:

R = ρ · l/S, S-sectional area; l-length.

If you take two conductors, their resistance when connected in parallel will be less due to the increase of the total section.

Current density and the heating conductor

For practical calculations of the operation modes of conductors applied the concept of current density – δ A/mm², it is calculated as follows:

δ = I/S, I-current, S – section.

The Current passing through a conductor heats it. More than δ, the greater the heat conductor. For wires and cables developed standards of acceptable density given the PUE (Rules for Electrical installation). For the conductors of the heating devices there are certain standards of density current.

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If the density of the δ above acceptable, may result in the destruction of the conductor, for example, overheating of the cable he destroyed the insulation.

Terms apply to calculate conductors for heating.

Methods of connection of conductors

Every handler is much easier to depict in the diagrams as electrical resistance R, then they are easy to read and analyze. There are only three ways of connections of resistances. The first method is the easiest way – a serial connection.

The photo shows that the total resistance is: R = R₁ + R₂ + R₃.

The Second way is more complicated – parallel connection. Calculate resistance in a parallel connection is performed in stages. Calculate the total conductance G = 1/R, then the total resistance R = 1/G.

You Can do another thing, first calculate total resistance in a parallel connection of resistors R1 and R2, after that repeat the operation and download R.

The Third method of connection is the most difficult – mixed connection, that is, present all the options considered. The scheme shown in the photo.

For the calculation of the scheme should be simplified, to do this, replace the resistor R2 and one R3, R2,3. It turns out the simple schema.

We can Now calculate the resistance in parallel connection, the formula of which is:

R2,3,4 = R2,3 · R4/(R2,3 + R4).

The Scheme is even easier, there are resistors with serial connection. In more complex situations, use the same conversion method.

Types of conductors

In electronics, in the production of printed circuit boards, the conductors represent thin strips of copper foil. Due to the short length of the resistance they have slightly, they in many cases can be neglected. For these conductors the resistance in parallel connection is reduced due to the increase of the cross section.

A Large section of the conductors represent wires. They are available in different diameters from 0.02 to 5.6 mm. For powerful transformers and electric motors produced copper, the shank of rectangular cross section. Sometimes when repairing replace the wire with a large diameter of several parallel-connected smaller.

A Special section of the conductors represent wires and cables industries offers a wide selection of brands for different needs. Often it is necessary to replace one cable into several, smaller sections. The reasons for this are very different, for example, cable cross-section 240 mm² it is very difficult to lay on road with steep bends. It is replaced by 2×120 mm², And the problem is solved.

Calculation of wires for heating

The Conductor heats the flowing current, if the temperature exceeds the allowable, there comes a destruction of insulation. The EMP provides the calculation of conductors for heating, the initial data for it are current, and environmental conditions in which is laid the conductor. According to these data from tables in PUE selected recommended conductor cross section (wire or cable).

In practice, there are situations when the load acting on the cable is greatly increased. There are twoexit ‒ to replace the cable on the other, it can be very expensive, or parallel to it to build another one to unload the main cable. In this case, the resistance of the conductor in parallel connection is reduced, thus decreases the heat.

To choose the right cross section of the second cable, use the tables in the EMP, it is important not to be mistaken with the definition of its operating current. In this situation the cooling of the cables will be even better than one. It is recommended to calculate resistance for parallel connection of two cables to more accurately determine their dissipation.

Calculation of conductors for a voltage loss

When the location of the consumer R_N at a large distance L from the source of energy U₁ there is quite a large voltage drop on the wires of the line. To the consumer R_N Supplied with voltage U₂ is much lower than the initial U₁. Practically the load performs a variety of electrical equipment connected to the line in parallel.

To solve calculate resistance in a parallel connection of all equipment is the load resistance R_N. Next, define the resistance of the wires of the line.

R_L = ρ · 2L/S

There's – a section of wire line, mm².

Next, the current in the line: I = U₁/(R_L + R_N). Now, knowing the current, determine the voltage drop on the wires of the line: U = I · R_L. Easier to find it as a percentage of the U₁.

U% = (I · R_L/U₁) · 100%

The recommended value U% is not more than 15%. The calculations are applicable for any current type.