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How does a resistor behave in an ac circuit – Resistor in ac circuit

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A circuit containing only resistor in AC circuit is known as Pure resistive AC circuit. The existence of inductance and capacitance does not exist in a pure resistance circuit. The AC current and voltage both move on and also backwards, both towards the circuit. As a result, the AC current as well as voltage have a sinusoidal waveform or is called a sinusoidal waveform.

In a pure resistive circuit, power is dissipated via the resistors as well as the phase of voltage and also current continues to be the same, i.e., both voltage and also current reach their maximum value at the same time. A resistor is a passive device that does not produce or consume power. It converts electrical energy into heat.

In an AC circuit, the voltage to current ratio relies on the supply frequency, phase angle and phase difference. In an AC resistive circuit, the value of the resistance of the resistor in ac circuit will certainly be the same despite the frequency of the supply.

The AC voltage applied in the circuit will be offered by the equation:

Then the instantaneous value of the current flowing through the resistor in ac circuit is as shown in the following figure:

ac resistor circuit
ac resistor formula

The value of the current will be maximum when ωt = 90 degrees or sinωt = 1

By placing the value of sinωt in the equation above, we get:

ac resistor formula 2

Phase angle and resistance waveform

Formula 1 and Equation 3 show that there is no phase difference in between the applied voltage and also the current flowing via a pure resistance circuit, i.e., the phase angle in between voltage and also current is zero. Hence, in an AC circuit including pure resistance, the current remains in phase with the voltage shown in the figure listed below.

ac resistor chart power voltage current

Power dissipated by a resistor in an ac circuit

The 3 colors red, blue and pink revealed on the power curve or waveform suggest the curve for current, voltage and also power specifically. From the indicator chart, it is clear that the current and voltage are in phase with each other, indicating that the current and voltage worths reach their peak at the same time, and the power contour is always positive for all current as well as voltage values.

As in a DC power circuit, the product of the voltage of the current is called the power in the circuit, similarly the power is likewise the very same in an AC circuit, the only distinction is that in an AC circuit the immediate value of voltage and current is thought about. The instantaneous power in a totally resistive circuit is given by the equation revealed below

Instantaneous power, p = vi

ac resistor power formula

The average power consumed in the circuit over the entire cycle is determined by the following equation:

ac resistor power formula

As a valve, cosωt is zero

By placing the value of cosωt in the equation above, the power value will be given by the transformed equation:

ac resistor power formula


  • P – average power
  • V r.m.s. – RMS value of supply voltage
  • I r.m.s. – RMS value of current

Thus, the power in a pure resistive circuit is given by:


The voltage and current in a pure resisting circuit are in phase with each other without phase distinction with a phase angle of no. The variable amount reaches a peak value in the interval of the very same duration in which the rising and falling voltage as well as current occur simultaneously.

Michal Pukala
Electronics and Telecommunications engineer with Electro-energetics Master degree graduation. Lightning designer experienced engineer. Currently working in IT industry.