# Understanding resistors in AC and DC circuit

Ohm’s law (V = IR) still applies in a circuit with a resistor and an AC power source. The passage of electric charge in only one direction is known as direct current (DC). It is the constant-voltage circuit’s steady state. The majority of well-known applications, on the other hand, rely on a time-varying voltage source. The flow of electric charge that occasionally reverses direction is known as alternating current (AC). The circuit is known as an alternating-current circuit if the source varies frequently, especially sinusoidally. Commercial and residential power, for example, meets a wide range of our demands. provides voltage and current vs time graphs for common DC and AC power. The AC voltages and frequencies that are routinely utilized in homes and businesses differ from country to country.

In this article, you’ll get to learn about resistors in AC and DC circuit, their formula, supplies, diagrams, calculation, and examples. You’ll also get to know the resistance between the AC and DC.

Contents

## AC and DC circuit resistors

The flow of electricity is unidirectional in Direct Current (DC). The polarity and direction of voltage and current in DC are always the same. The battery is used to generate direct current. In Alternating Current (AC), on the other hand, the flow of electric charge occasionally reverses direction. Over time, the polarity of the voltage in AC switches from positive to negative. Because of the change in the current direction, the voltage polarity has shifted.

AC is a type of electricity that is used to power homes, businesses, and other establishments. Although sine wave is the most frequent type of AC supply, other waveforms such as triangular wave, square wave, and sawtooth wave are also used in some applications.

Resistance is a quality of a substance or material that prevents electricity from flowing through it. OR, resistance is the ability of a circuit or element (called a resistor) to resist current flow through it. Wood, air, mica, glass, rubber, tungsten, and other materials are examples of high-resistance resistors. The unit of resistance is “Ohm,” which is defined by Ω and represented by the letter “R.”

##### Diagram of AC and DC resistor circuit: ## Difference between AC and DC resistance

### AC resistance

Impedance is the term used to describe resistance in AC circuits. Impedance in AC circuits is the total resistance (resistance, inductive reactance, and capacitive reactance) (Z). When AC flows through a wire (resistor, inductor, or capacitor), it creates a magnetic field across that wire that resists the flow of AC Current as well as the resistance of that wire. This opposing cause is referred to as inductance. The property of a coil (or wire) that opposes any rise or reduction in current or flux through it is called inductance. We also know that inductance exists only in AC since the magnitude of current changes constantly.

The property of a coil of wire in an AC circuit that opposes the change in current is known as inductive reactance XL. Inductive reactance has the same unit as capacitive reactance, namely Ohm (Ω), although the corresponding symbol for capacitive reactance is XL.

In a capacitive circuit, Capacitive Reactance is the opposition to current flow is solely AC circuits. The unit of capacitive reactance is the same as that of resistance and inductive reactance, namely Ohm (Ω), however, the corresponding symbol is XC.

#### AC Resistance Measurement

Electrical Resistance & Impedance Formulas in AC Circuits

In AC Circuits (Capacitive or inductive Load), Resistance = Impedance i.e., R = Z

Z = √ (R2 + XL2) … In case of Inductive Load

Z = √ (R2 + XC2) …In case of Capacitive Load

Z = √ (R2 + (XL– XC)2…In the case of both inductive and capacitive Loads.

Where;

X= Inductive reactance

X= 2πfL…Where L = Inductance in Henry

And;

XC = Capacitive reactance

XC = 1/2πfC… Where C = Capacitance in Farads.

Furthermore, on AC circuits, the Sinusoidal wave is the most used type of AC supply. A typical AC voltage is described by the mathematical function.

V (t) = VMax sin ωt. Where:

V (t) is the voltage in the function of time. The voltage changes with time.

t is the variable time in seconds.

VMax is the peak value that the sine wave can reach in both positive and negative directions. For the positive cycle, it is VMax and for the negative cycle, it is -VMax.

ω is the angular frequency. ω = 2πf.

f is the frequency of the sine wave.

### DC resistance

In DC circuits, there is no conception of inductive and capacitive reactance. Because DC circuits have no frequency and the amplitude of DC is constant, capacitive and inductive reactance in DC circuits is zero. As a result, only the wire’s original resistance is used. As a result, the resistance of a wire is lower for DC than AC, thus AC lines require more insulation than DC lines.

#### DC Resistance Measurement

Electrical Resistance Formulas. In DC Circuits, we calculate the resistance by Ohm’s Law.

R = V/I.

If you’re trying to figure out which resistance to using in an electric circuit and you’re not sure whether to use AC or DC, take AC if the current is AC and DC if the current is DC.

For DC circuits, the determination of current, voltage, and power in DC circuits is performed using Ohm’s law. Both voltage and current polarities are considered to be constant in this example. The values of inductance and capacitance in pure resistive AC circuits are insignificant. As a result, current, voltage, and power will be calculated using the same Ohm’s law and Kirchhoff’s Circuit rules. The distinction is in the use of RMS value or instantaneous peak to peak value.

Read more: Understanding wire wound resistor

##### AC or DC resistance, which one is more:

As previously stated, the frequency of the DC supply is zero, hence there is no skin effect (a behavior of alternating current to flow through the surface i.e., the outer layer of a conductor instead of the core of the wire). when used in DC circuits AC resistance in AC circuits is higher than DC supply in DC circuits due to the skin effect.

### Skin Effect Formula:

δ = √(2ρ/ωµ)

Where;

δ = Skin effect depth

ρ = Specific resistance

ω = 2πf = Angular frequency

µ = Permeability of the conductor

In summary, frequency and skin effect are directly related, i.e., if frequency increases, skin effect increases as well, whereas, in DC, neither frequency nor skin effect exists.

As a general rule; AC Resistance = 1.6 x DC Resistance.

Read more: Understanding metal oxide film resistors

## Resistor with DC and AC supplies

A passive device is a resistor. It doesn’t use or generate any energy. Electrical energy is used here. However, a resistor wastes electrical energy as heat. Below is a resistor with a DC power supply. The resistance, which is the voltage to a current ratio in DC resistive circuits, is linear.

Below is a resistor with an AC power supply. The voltage to a current ratio in AC circuits is primarily determined by the supply frequency f and phase angle or phase difference. As a result, the term Impedance is used to describe resistance in AC circuits since it has both magnitude and phase, whereas resistance in DC circuits just has magnitude. Impedance is represented by the letter Z.

Read more: Understanding resistor color codes

## Examples of Resistors in AC Circuits

### Example 1

Using the following circuit. A resistive heating element is coupled to a 240 V AC power supply. The heating element consumes 1.2 K Watts of power. The resistance of the heating element can be estimated using the formula Current flowing through the heating element is

I = P / V

P = 1.2 K Watts = 1200 Watts.

V = 240 V.

Therefore I = 1200 / 240 = 5 Amps.

The value of the heating element’s resistance can be estimated using Ohm’s law as follows:

R = V / I

R = 240 / 5 = 48Ω.

### Example 2

Consider the following circuit where A resistor of resistance 47 Ω is connected to a supply of 120 V. The current flowing through the resistor and the electricity it consumes can be computed as follows: Ohm’s law can be used to compute the current flowing through the resistor.

I = V / R

I = 120 / 47 = 2.55 Amps.

The power consumed by the resistor is

P = I2 * R = V2 / R

P = 1202 / 47 = 306 Watts.