Real and reactive components of current?

[debwaldy]

Real and reactive components of current??

Homework Statement

Hi there. so I am trying to solve this problem but i don't understand some of the terms used,which is obvoiusly causing some trouble. Any explanation of the terms or help would eb much appreciated.
A coil having a resistance of 20 ohms and an inductance of 0.15 henry is connected in series with a 100*10^-6 Farad capacitor across a 230 V 50 Hz supply.
Calculate:
the active and reactive components of the current

Homework Equations

I'm not too sure because i don't know what active and reactive current is? but i would start by calculating the capacitive and inductive reactance...or?

The Attempt at a Solution

I know how to calculate active and reactive power if given I and V and power factor,but not all these quantities are given in the question.
thanks in advance

 

[anathema]

Dear student,

Thank you for reaching out for help. The terms "real" and "reactive" components of current refer to the two components of alternating current (AC) that are in phase with the voltage and those that lag or lead the voltage, respectively. In other words, the real component represents the current that is used to do useful work (i.e. active power) while the reactive component represents the current that is used to establish and maintain magnetic and electric fields (i.e. reactive power).

To calculate the real and reactive components of current in this problem, you will need to first calculate the total impedance of the circuit, which is the combination of the resistance, inductive reactance, and capacitive reactance. The formula for total impedance is Z = √(R^2 + (Xl - Xc)^2), where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance.

Once you have calculated the total impedance, you can use Ohm's law (I = V/Z) to find the total current in the circuit. This current will have both real and reactive components.

To calculate the real component of current, you can use the formula Ireal = Icosθ, where θ is the phase angle between the voltage and current. This phase angle can be found using trigonometry, specifically the inverse tangent function (tan^-1).

To calculate the reactive component of current, you can use the formula Ireactive = Isinθ.

I hope this helps you understand the problem better and gives you a starting point for solving it. If you have any other questions or need further clarification, please don't hesitate to ask.

 

[ogb p]

The terms "active" and "reactive" components of current refer to the different types of current that flow in a circuit. Active current, also known as real or true current, is the component that is responsible for producing useful work in a circuit. It is in phase with the voltage and is measured in amperes (A). Reactive current, on the other hand, is the component that does not produce useful work but is necessary for the operation of certain components in the circuit. It is out of phase with the voltage and is measured in reactive volt-amperes (VAR).

To calculate the active and reactive components of the current, you will need to use the following equations:

Active current (I) = Voltage (V) / Resistance (R)
Reactive current (I) = Voltage (V) / Reactance (X)

To find the reactance, you will need to calculate the inductive reactance (XL) and capacitive reactance (XC) using the following equations:

Inductive reactance (XL) = 2πfL
Capacitive reactance (XC) = 1/(2πfC)

Where:
f = frequency of the supply (50 Hz in this case)
L = inductance of the coil (0.15 henry)
C = capacitance of the capacitor (100*10^-6 Farad)

Once you have calculated the active and reactive components of the current, you can use them to find the active and reactive power using the following equations:

Active power (P) = Voltage (V) x Active current (I) x Power factor (cosθ)
Reactive power (Q) = Voltage (V) x Reactive current (I) x Power factor (sinθ)

Where:
Power factor (cosθ) = Active power (P) / Apparent power (S)
Power factor (sinθ) = Reactive power (Q) / Apparent power (S)
Apparent power (S) = Voltage (V) x Total current (I)

I hope this helps clarify the terms and equations used in the problem. Good luck with your calculations!