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What is a Pure(ly) Resistive Circuit and What are its Characteristics?

Close-up of details on a circuit board with resistors


Long before the Borg uttered one of my favorite phrases, "Resistance is Futile," I understood the effects resistance has on all aspects of our lives. Furthermore, even my earliest memories from childhood contain teachings from Bible school that made an emphasis on the resistance to temptation.

Moreover, one of the best examples of the importance of resistance and its effects is the existence of a group of formulas called Ohm's Law. As I am sure you are aware, Ohm's law is a set of equations that one can use to calculate the relationship between current, resistance, and voltage within an electrical circuit. So, yes, resistance affects every aspect of our lives, from religion to the field of electronics.

Furthermore, in terms of an electrical circuit, the property or characteristic of being resistive can also define a circuit as a whole. Also, the type of electrical circuit I am referring to is called a Pure(ly) Resistive Circuit.

What are Pure Resistive Circuits?

A purely resistive circuit is a circuit that has inductance so small that at its typical frequency, its reactance is insignificant as compared to its resistance. Furthermore, in a purely resistive circuit, the whole of the utilized voltage is consumed in overcoming the ohmic resistance of the circuit itself. Also, another name for a purely resistive circuit is a non-inductive circuit.

Moreso, in a purely resistive circuit, the phase angle between current and voltage is zero. Additionally, if we were to express the instantaneous current and instantaneous applied voltage of a typical purely resistive circuit, it will indicate that the supplied voltage and current are indeed in phase with each other.

Furthermore, if we examine a graphical representation of the same circuit, we can see from its power curve that no part of the power cycle becomes negative at any time. Therefore, in a purely resistive circuit, the power is never zero. Moreover, this is due to the instantaneous values of the current and voltage being always negative or positive. Also, the frequency of the purely resistive circuit's power cycle is double that of the current and voltage waves.

Graphic of circuit resistance

The relationship between current and voltage depicts what kind of resistance your circuits are working with.


The Purely Resistive AC Circuit

A circuit that contains only a pure resistance (ohms) in an AC circuit is called a Purely Resistive AC Circuit. From a technical standpoint, this circuit does not contain capacitance or inductance. The alternating voltage and current moves synchronously forward in addition to backward in either direction of the circuit. Therefore, the alternating voltage and current exhibits the shape of a Sine wave and is thus called a sinusoidal waveform.

In these circuits, the resistors dissipate the power, while the phase of the current and voltage remain the same. The current and the voltage achieve their maximum value simultaneously. It is worth noting that a resistor is a passive component, and it neither produces nor consumes electrical power. So, what effect does a resistor have on the power within a purely resistive circuit? It converts the available energy into heat.

As I am sure you are aware, in an AC circuit, the ratio of the current to the voltage is dependent on the phase angle, phase difference, and supply frequency. Furthermore, a resistor's resistance value will remain constant regardless of the supply frequency.

The Pure Resistive Circuit in More Detail

As we examine the power in a purely resistive circuit, we can observe from the below waveforms (red, blue, and pink), the overall characteristics of a typical circuit. From the analytic representation, it is evident that the voltage and current are in phase with each other. You can also observe that the value of the voltage and current both achieve their maximum simultaneously. And you can ascertain that the power curve is consistently positive for all values pertaining to the voltage and current.

Waveforms of voltage, current, and power based on resistances.

Waveforms are helpful representations of any expected output or input for a circuit.

I am sure you recall that in a direct current (DC) supply circuit, the byproduct of current and voltage is still called the Power. Although it is the same in an AC circuit, the difference here is, in an AC circuit, we take into consideration the instantaneous value of current and voltage. Therefore, the instant power we find in a purely resistive circuit, we represent by the following equation.

Instantaneous power, P = VI 

The Power Factor of Pure Resistive Circuits

Firstly, what is meant by the phrase power factor? Well, in electrical engineering, we define the power factor (PF or cosφ) as the ratio between the power that you can use in an electric circuit (real power, P) and the power calculated from multiplying the voltage and current in a circuit (apparent power, S). Furthermore, we define a PF as having a range from zero to one.

In a DC circuit, the result of V x I gives us the power (P) in watts (W) drawn by a circuit. However, in an AC circuit, this will deviate. Because in an AC circuit, the result of V x I gives us the apparent power (S) and not the real power (P) since the current and voltage are not in phase.

We can further define the PF in an AC circuit as follows:

  1. Define the PF as the cosine of the phase angle between current and voltage

  2. Define the PF or cos φ as resistance (R) ÷ impedance (Z)

  3. PF or cos φ is also defined as: real power (P) ÷ apparent power (S)

Therefore, since the voltage and current are in phase for a purely resistive circuit, its PF is 1.

With pure inductive or pure capacitive circuits, the current is 90o out of phase with the circuit voltage; thus, the cos φ = 90o. Hence, the PF of these circuits is zero. The PF of the RLC series circuit lies between zero and one.

The purely resistive circuit has unique characteristics that deviate from those of other circuit types. However, without these types of circuits, devices like Incandescent Lamps would not be possible. 

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