Electric circuits with active resistances can first be simplified by combining resistors connected in parallel or in series into common resistances equivalent to them, and then, using Ohm's law, find the current or voltage on the calculated total resistance. After this, you can go the opposite way and using Ohm's law find the voltage and current at each of the circuit resistances.

The equations necessary for calculations are given in the article before specific examples. The information in the article is enough to calculate the electrical circuits yourself. In cases where several steps are necessary, they are given sequentially.

All resistances in the circuit are shown as resistors (depicted as a zigzag line). It is assumed that the resistance of the wires connecting them (shown as straight lines) is zero (at least approximately, compared to resistors).

All the main steps for circuit design are given below.

- 1 If the circuit contains more than one resistor, find the equivalent resistance "R" of the entire circuit according to the method described below in the section "Resistors connected in series and in parallel."
- 2 Substitute the found total circuit resistance "R" in the equation for Ohm's law, as described below in the Ohm's Law section.
- 3 If the circuit contains more than one resistor, the voltage or current values found in the previous step can again be substituted into the equation for Ohm's law by finding the voltage or current on any circuit resistor.

Ohm's law can be written in three equivalent forms, depending on what needs to be determined:

"V" - voltage ("potential difference") *on* resistance, "I" is the current flowing through the resistance, and "R" is the resistance value. If the resistance is *resistor* (a circuit element having a specific electrical resistance), it is usually indicated by the letter "R" with the addition of a number, for example, "R1", "R105", etc.

It is easy to pass from formula (1) to formula (2) or (3) by algebraic transformations. In some cases, the designation "E" is used instead of "V" (for example, **E = IR**), where "E" means EMF, or "electromotive force", which is another name for voltage.

Equation (1) is used when the current flowing through a certain resistance is known.

Equation (2) is suitable for cases where the voltage at a given resistance is known.

Equation (3) allows you to calculate the unknown value of the resistance, if the current passing through this resistance and the voltage on it are known.

In the international system of units (), the values included in Ohm's law are measured in the following units:

- The voltage across the resistance "V" is defined in, abbreviated "B".
- The current "I" is measured in, denoted as "A".
- Resistance "R" is measured in ohms, abbreviated "Ohm." If the letter "k" is before the designation Ohm, it means "thousand" ohms, or kiloomes, if the letter "M" is "million" ohms, or megaoms.

Ohm's law applies to any circuit containing only active resistances (such as resistors, or conductors with their own non-zero resistance, or computer units). For some elements of the circuit (inductors and capacitors), Ohm's law is not applicable in the above form (in the equations above, the resistance contains only "R" without taking into account the elements of inductance and capacitance). Ohm's law can be used for circuits with active resistance, regardless of whether a constant resistance (current), alternating resistance (current), or any arbitrary waveform that varies with time is attached to them (or passes through them). If the supplied voltage or current changes in a sinusoidal manner (with a frequency of, for example, 50 Hz, as in a home electrical outlet), they are usually measured in rms volts or amperes.

You can find more information about Ohm's law in

### Example: Voltage drop along the wire

Suppose we want to find the voltage drop across a piece of wire when a current of 1 ampere flows through it. The resistance of this section of the wire is 0.5 ohms. Using equation (1) for Ohm's law given above, we calculate the voltage drop:

**V** = **IR** = (1 A) (0.5 Ω) = 0.5 V (i.e. 1/2 volt)

If the rms power of an alternating current with a frequency of 50 Hz (home network) is 1 ampere, the result is the same, 0.5 V, but this will be the "rms" value of the ac voltage drop.

## Series Resistance

A "series" connection of resistances is one in which the end of the previous resistor is connected to the beginning of the next, and thus the resistors form a chain (see figure), the total resistance of such a chain is equal to the sum of the resistances of all its constituent resistors. In the case of "n" resistors R1, R2,. Rn we have:

## Parallel Resistance

The total resistance of the resistors connected *parallel* (see diagram on the right) is equal to:

Two slashes ("//") are often used to indicate that resistances are connected in parallel. For example, the parallel connection of resistors R1 and R2 can be briefly referred to as "R1 // R2". Note that R1 // R2 = R2 // R1. The parallel connection of the three resistances R1, R2 and R3 is indicated as "R1 // R2 // R3".

### Example: parallel-connected resistances

In the case of two identical resistors R1 = 10 Ohms and R2 = 10 Ohms connected in parallel, we have:

1 / R_{the general} = 1 / R1 + 1 / R2 = 0.1 + 0.1 = 0.2 R_{the general} = 1 / 0.2 = 5 ohms

It is also useful to remember the “less than least” rule, which means that the resulting resistance will be lower than the lowest resistance in a given connection.

## Resistances connected in series and in parallel

Circuits that include various combinations of resistances connected both in series and in parallel can be calculated by combining the resistors into an “equivalent” or “common” resistance.

- Combine all resistors connected in parallel into their equivalent resistance, using the “Resistance in parallel connection” section above. Note that if the parallel-connected branches contain series-connected resistors, you must first find the equivalent resistance for these series-connected resistors.
- Combine the series resistors to find the total resistance of the circuit R
_{the general}. - Using Ohm's law, find the total current through the circuit at a given voltage, or the total applied voltage at a known current through the circuit.
- The total voltage or current calculated above is used in the equations of Ohm's law when calculating voltages and currents in individual sections of the circuit.
- Substitute the previously found values of current or voltage into the equations of Ohm's law in order to find the current or voltage on a single resistor. This operation is illustrated in the example below.

For large circuits, the 2 steps described above may need to be applied several times.

#### Example: a chain of serial and parallel connections

In the case of the circuit shown on the right, you must first combine the parallel-connected resistors, finding their equivalent resistance R1 // R2, and then find the total resistance of the circuit according to the formula:

Let R3 = 2 Ohms, R2 = 10 Ohms, R1 = 15 Ohms, and the circuit is connected to a 12-volt battery, so that V_{the general} = 12 volts. According to the steps described above, we have:

R_{the general} = R3 + R1 // R2 = 2 + 6 = 8 Ohms

Now the voltage across resistance R3 (denoted as V_{R3}) can be calculated using Ohm's law, since the current flowing through this resistance is known and is equal to 1.5 amperes:

V_{R3} = (I_{common}) (R3) = 1.5 A x 2 Ohms = 3 V

The voltage on resistor R2 (equal to the voltage on resistor R1) can be calculated using Ohm's law by multiplying the current I = 1.5 amperes by the equivalent resistance of the parallel connection of resistors R1 // R2 = 6 Ohms, which gives 1.5 x 6 = 9 volts , or find by subtracting the voltage at R3 (found above V_{R3}) of the total applied voltage of 12 volts, i.e. 12 volts - 3 volts = 9 volts. After that, you can find the current through R2 (designated as I_{R2}) using Ohm's law (voltage on R2 is denoted as "V_{R2}"):

I_{R2} = (V_{R2}) / R2 = (9 volts) / (10 Ohms) = 0.9 amperes

The current through R1 can be found in a similar way, dividing the voltage on this resistor (9 volts) by its resistance (15 Ohms), which gives a result of 0.6 amperes. Please note that the current through R2 (0.9 amperes) in total with the current through R1 (0.6 amperes) gives the total current through the circuit (1.5 amperes).

## Where and when can Ohm's law be applied?

Ohm's law in the aforementioned form is valid over a fairly wide range for metals. It is performed until the metal begins to melt. A less wide range of application in solutions (melts) of electrolytes and in highly ionized gases (plasma).

When working with electrical circuits, sometimes it is necessary to determine the voltage drop on a particular element. If it is a resistor with a known resistance value (it is put on the case), and the current passing through it is also known, you can find out the voltage using Ohm's formula without connecting a voltmeter.

## Ohm's Law

Ohm's law can be written in three equivalent forms, depending on what needs to be determined:

"V" - voltage ("potential difference") *on* resistance, "I" is the current flowing through the resistance, and "R" is the resistance value. If the resistance is *resistor* (a circuit element having a specific electrical resistance), it is usually indicated by the letter "R" with the addition of a number, for example, "R1", "R105", etc.

It is easy to pass from formula (1) to formula (2) or (3) by algebraic transformations. In some cases, the designation "E" is used instead of "V" (for example, **E = IR**), where "E" means EMF, or "electromotive force", which is another name for voltage.

Equation (1) is used when the current flowing through a certain resistance is known.

Equation (2) is suitable for cases where the voltage at a given resistance is known.

Equation (3) allows you to calculate the unknown value of the resistance, if the current passing through this resistance and the voltage on it are known.

In the international system of units (SI), the values included in Ohm's law are measured in the following units:

- The voltage across the resistance "V" is determined in volts, abbreviated to "V".
- The current "I" is measured in amperes, denoted as "A".
- Resistance "R" is measured in ohms, abbreviated "Ohm." If the letter "k" is before the designation Ohm, it means "thousand" ohms, or kiloomes, if the letter "M" is "million" ohms, or megaoms.

Ohm's law applies to any circuit containing only active resistances (such as resistors, or conductors with their own non-zero resistance, or computer units). For some elements of the circuit (inductors and capacitors), Ohm's law is not applicable in the above form (in the equations above, the resistance contains only "R" without taking into account the elements of inductance and capacitance). Ohm's law can be used for circuits with active resistance, regardless of whether a constant resistance (current), alternating resistance (current), or any arbitrary waveform that varies with time is attached to them (or passes through them). If the supplied voltage or current changes in a sinusoidal manner (with a frequency of, for example, 50 Hz, as in a home electrical outlet), they are usually measured in rms volts or amperes.

You can find more information about Ohm's law on Wikipedia.

### Steps Edit

- Combine all resistors connected in parallel into their equivalent resistance, using the “Resistance in parallel connection” section above. Note that if the parallel-connected branches contain series-connected resistors, you must first find the equivalent resistance for these series-connected resistors.
- Combine the series resistors to find the total resistance of the circuit R
_{the general}. - Using Ohm's law, find the total current through the circuit at a given voltage, or the total applied voltage at a known current through the circuit.
- The total voltage or current calculated above is used in the equations of Ohm's law when calculating voltages and currents in individual sections of the circuit.
- Substitute the previously found values of current or voltage into the equations of Ohm's law in order to find the current or voltage on a single resistor. This operation is illustrated in the example below.

For large circuits, the 2 steps described above may need to be applied several times.

## The meaning of Ohm's Law

Ohm's law determines the current strength in an electric circuit at a given voltage and known resistance.

It allows you to calculate the thermal, chemical and magnetic effects of the current, since they depend on the current strength.

Ohm's law is extremely useful in engineering (electronic / electrical), as it relates to three basic electrical quantities: current, voltage, and resistance. He shows how these three quantities are interdependent at the macroscopic level.

If it were possible to characterize Ohm's law in simple words, then it would visually look like this:

From Ohm's law it follows that it is dangerous to close a conventional lighting network with a low resistance conductor. The current strength will be so large that it can have dire consequences.