**AC through pure resistance | Pure resistive load | power circuit in pure resistive load | Instantaneous power of pure resistive load | Average power of a Pure Resistive load | power factor in case of pure resistive load or resistance|**

## Introduction:

As we know, in a previous post, we discussed AC fundamentals, in which we discussed maximum value, peak value, average value, peak factor, form factor, etc. In this post, we will look at how a pure resistance behaves when connected to an alternating current supply.

## AC through pure resistance:

In the case of pure resistance, we connect a pure resister to an alternating current supply. As you can see in the image below,

There is a pure resistor connected to an AC supply source. The supply voltage is denoted by “v,” and its value is **V _{m}sinωt**. And due to the load, a current “i’ is flowing through the resistive load. To find out the current value, we will do a calculation, which is given below.

Calculation

From the above calculation, we find out the value of current, which is equal to **I _{m}sinωt**. So, now we have two equations:

**v = V _{m} sin ωt**

**i = I**

_{m}sin ωtThere are no changes in the phase angle (ωt) now that we can see the voltage and current equations. So, it is confirmed that the two quantities, voltage and current, are in the same phase. It means there is no angle difference between a voltage phaser and a current phaser. So, the phase angle will be zero.

## Graphical approach:

We know that when the phase angle is zero, it means both signals will be in the same phase. When the voltage phaser starts at zero magnitude, the current phaser line also starts at this point. And when the voltage phaser graph reaches its maximum magnitude, the current phase also reaches its maximum point.

## Power factor in the case of pure resistance or resistive load:

Basically, power factor is **cos φ** value, and the angle **φ** is the angle between the main voltage phaser and the main current phaser. In the case of a pure resistive load, the phase angle is zero. So, the power factor value is **cos φ = cos 0° = 1** unity.

## Power circuit with a pure resistive load:

There are two types of power.

- Instantaneous power
- Average power

## Instantaneous power:

Instantaneous power is indicated by ‘p’ and the instantaneous power calculation is given below.

As you can see, instantaneous power’s value. In which there are two values, the first of which is a constant value and the second of which is a symmetrical value. Because of the constant value and symmetrical value, this signal is periodic. When a signal is made with the constant value and the symmetrical value, the signal is unsymmetrical but periodic.

In the instantaneous value,** 2ωt** indicates that the instantaneous power frequency is two times that of the input supply voltage frequency, and the time period of the instantaneous power will be half of the input supply voltage.

## Graphical approach:

There is a three-signal graph in the image, which is given below. These are the voltage, current, and instantaneous power graphs.

According to the graph, you can see that the time period of the voltages and currents is **2π**. But instantaneous power’s graph is **π** only. The time period indicates that the signal has completed one cycle.

## Average power:

Average power can be defined by means of instantaneous power. And it doesn’t depend on frequency. So, average power is the constant value of instantaneous power’s value. It means total average power of the pure resistive circuit is **P _{av }= V_{rms}.I_{rms}** . A wattmeter measures average active power.

## Summary:

To summarize, you can note down some important points regarding pure resistive load in AC supply.

### In the case of AC through pure resistance load:

- The phase angle between the voltage phaser and the current phaser is zero.
- Because the phase angle is zero, the power factor is unity, which is very good.
- The frequency of instantaneous power is twice the frequency of the input supply.
- Wattmeter measure average active power.
- The value of average active power doesn’t depend on the supply frequency. or average active power is zero in the case of a symmetrical waveform.

## Conclusion:

In the whole post, we should notice that the power factor of the pure resistive load is unity, which is perfect. But this is only a theoretical value. Practically, there is no load present that is purely resistive. Every resistive load has some inductive quality involved. Most of the domestic load is an R-L type of load