# Resistance in AC Circuits

Resistance in AC Circuits can be used by giving rms values of voltage, current and consumed power.

In our previous articles, we looked at the connections of resistances and used the Ohm Act to calculate the voltage, current and power associated with them.In any case, both the voltage and the current are assumed to be in a constant polarity, flow and direction, that is, **Direct Current** or **DC.**

However, it is another type of feed known as alternating current or **AC,** which reverses the voltage from positive to negative and over time, and can also release the current back and forth according to the voltage.The oscillation pattern of an AC source follows the mathematical form of a "sinus wave", commonly called the **Sinusoidal WaveForm.**Therefore, a sineoidal voltage can be defined as **V(t) = V _{max} sin ωt. **

When using pure resistors in AC circuits with negligible inductance or capacitance values, the same principles of the Ohm Act, circuit rules for voltage, current and power (and even Kirchhoff Laws) apply as in DC-resistant circuits, this time the only difference is in the use of instantaneous "top-to-bottom" or "rms" amounts.

When working with AC alternating voltages and currents, it is usual to use only "rms" values to avoid confusion.The rms or "root average square" value of an AC waveform is the effective or DC value equivalent to an AC waveform.In addition, the schematic symbol used to identify an AC voltage source is a battery symbol for DC, while in AC circuits it is a "wavy" line, which is shown below.

### Symbol Representation of DC and AC Consumables

Resistances are "passive" devices, that is, they do not produce or consume electrical energy, they simply convert electrical energy into heat.In DC circuits, the linear ratio of voltage in a resistance to the current is called resistance.However, the ratio of this voltage to current in AC circuits depends on the frequency of the feed and the phase difference or phase angle (φ).Therefore, when using resistors in AC **circuits, the term Impedance** is used, usually **the symbol Z** is used, and we can say that dc resistance = AC impedance, R = Z.

When used in AC circuits, it is important to note that, unlike capacitors and inductors, a resistance will always have the same resistance value, regardless of the frequency of supply from DC to very high frequencies.

For resistors in AC circuits, the direction of the current passing through them has no effect on the behavior of the resistance, so the voltage rises and falls as it rises and falls.The current and voltage reach the maximum at exactly the same time, fall to zero and reach the minimum. that is, they rise and fall at the same time and are said to be "co-phased", as shown below.

### VI Phase Relationship and Vector Diagram

At any point along the horizontal axis, since the current and voltage reach their maximum values at the same time, we can see that the instantaneous voltage and current are in the same phase, that is, the phase angle is ε 0 ^{o. }Then these instant voltage and current values can be compared only to give the omic value of resistance using the ohm law.Consider the circuit consisting of an AC source and a resistance:

The instantaneous voltage on the resistance, V _{R,} the supply voltage, the V _{t} equals and is given as follows:

The instantaneous current flowing in the resistance will therefore be as follows:

Since the voltage on a resistance is given as V_{R} = IR, the instantaneous voltage on the above resistance can also be given as follows:

In fully resistant serial AC circuits, all voltage drops between resistors can be added together to find the total circuit voltage, since all voltages are in the same phase as each other.Similarly, in a fully resistant parallel AC circuit, all separate branch currents can be combined to find the total circuit current, since all branch currents are in the same phase as each other.

Since the phase angle between voltage and current for resistances in AC circuits is zero φ, the power factor of the circuit is given as cos 0^{o} = 1.0.At any given moment, the power in the circuit can be found by multiplying the current and voltage at that moment.

The power (P) consumed by the circuit is then given as P = Vrms Ι cos Φ in watts.However, since cos(Φ) = 1 in a fully resistant circuit, the power consumed is simply given as follows, P = Vrms is the same as the Ohm Act.

This then gives us the waveform "Power" and is shown below as a series of positive pulses, since when the voltage and current are both in the positive half of the cycle, the resulting power is positive.When both voltage and current are negative, the multiplication of two negative values gives a positive force pulse.

Then, the power expended on a fully resistant load fed from an AC RMS source is the same as a resistance attached to a DC resource and is given as follows:

- Here:
- P is the average power in Watts
- V
_{rms}is the supply voltage of rms in Volts - I
_{rms}is the rms feed current in amps - R is the resistance of resistance in Ohm (Ω) – it must be Z to indicate impedance

The heating effect produced by an alternate current with a maximum Imax value is not the same as that of a DC current of the same value.Rms values should be used to compare ac heating effect with an equivalent DC.Power tools, toasters, kettles, irons, etc. Any resistant heating element such as a resistant AC circuit can be classified as a resistant AC circuit.

### Resistance Question Sample in AC Circuits 1

A 1000 Watt (1kW) heating element is connected to the 250v AC supply voltage.Calculate the impedance (AC resistance) of the element when it is hot and the amount of current taken from the feed.

## Resistance Question Sample in AC Circuits 2

Calculate the power consumed by a 100Ω resistant element connected to a 240v source.

Because there is only one component connected to the resource, V _{R} = V _{S}

To summarize, in a pure omic AC Resistance, it is said that the current and voltage are both "in-phase" because there is no phase difference between them.The current flowing from the resistance is directly proportional to the voltage on it with this linear relationship called impedance in an AC circuit.As with DC circuits, the Ohm Act can be used when working with resistors in AC circuits to calculate resistance voltages, currents and power.