Capacitive Reactance Calculator and Tutorial

Capacitive reactance is the capacitor equivalent to the resistance of a resistor. Unlike a resistor, a capacitor's reactance is inversely proportional to frequency. A capacitor exhibits an infinite reactance to a DC (0 Hertz) signal. As frequency goes up, the capacitive reactance will go down. At very high frequencies the capacitive reactance of circuit approaches zero.

The formula for calculating capacitive reactance is:

Equation 1: Xc = 1/(2*PI*F*C)

where

Xc is the capacitive reactance in Ohms
PI is the constant 3.14
F is the frequency in Hertz
C is the value of the capacitor in Farads

Capacitance Reactance Calculator

You can see how the capacitive reactance changes with frequency and capacitance using the capacitance reactance calculator below. Enter in the capacitance in uF and the frequency. If you enter in 0 for the frequency the calculator calculates an answer of infinity. If you want to change the frequency easily, after you enter a number in the frequency box, simply hold down the up or down arrow keys on your keyboard.

Capacitance Reactance Calculator

Capacitance (uF)
Frequency (Hz)   
Capactive Reactance Ohms :

Resistors in Parallel: Electronics Tutorial #10, BookMarkTutoring.com

Placing resistors in parallel reduces the overall resistance of a circuit. The equation for calculating the equivalent resistance of two or more resistors in parallel is

Equation 1: Req = 1/(1/R1 + 1/R2 + 1/R3 + ..... + 1/Rn) 

For the circuit shown below, where R1 = 2 Ohms, R2 = 4  Ohms and R3 = 4 Ohms, the equivalent resistance calculated with equation 1 is 

Req = 1/(1/R1 + 1/R2 + 1/R3)

Req = 1/(1/2 + 1/4 + 1/4) = 1/(6/12 + 3/12 + 3/12) = 1/(12/12) = 1 Ohm 

The equivalent resistance of resistors in parallel is always lower than the lowest value resistor

Circuit Applications

Resistors are often placed in parallel to construct a resistor that doesn't come in a standard value or, in many cases, to allow the use of resistors with lower power ratings. When resistors are placed in parallel the current splits between the different branches in the parallel circuit. The amount of current in each branch is proportional to the resistance in each branch. Branches with lower resistance will conduct more current. 

Another reason to place resistors in parallel is  even heat distribution. Current flow results in energy dissipation which in turn results in heat. If one resistor is used instead of several resistors in parallel the heat will be more concentrated on the circuit board. As well, the large resistor will need a higher power rating. The higher levels of concentrated heat may result in a design that has a lower mean time between failure. This can be especially true in designs that must carry a significant amount of current. 

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Voltage Dividers: Electronics Tutorials #9

A voltage divider is most often used to provide a voltage that is a fraction of a battery voltage. It most often consists of two resistors that are connected in series with a battery.  The ratio of the resistors determines the output voltage from the voltage divider.

The formula for calculating the output voltage of a voltage divider with two resistors connected to a battery is

Equation 1:  Vout= Vbattery*R2/(R1 + R2) 

The circuit diagram below shows a voltage divider connected to a 10 V battery.  With the 2000 and 3000 ohm resistors, the output voltage is calculated  from equation 1 as

Vout = 10*3000/(2000 + 3000) = 6 Volts

The idea can be extended to any number of resistors to obtain any fractional output voltage desired.  The formula comes about by dividing the applied voltage across the total series resistance to obtain the current. In the example above the current is 2 mA (10V/5000 Ohms). The current multiplied by the resistor will give the voltage drop across the resistor.

Voltage Buffers

Often when a voltage divider is used to supply a different voltage than a battery voltage, a voltage buffer is placed at the output voltage node of the voltage divider.   A voltage buffer, because it does not draw any current (or very little), will not change the output voltage of the voltage divider. Voltage buffers are often made from transistor devices such as JFETs and MOSFETs.

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Inductors in Series: Electronics Tutorial #8, BookMarkTutoring.com

Inductors in series add. The formula for inductors in series is

Equation 1: Leq = L1 + L2 + L3 + ...... Ln

In the figure below, the equivalent inductance is calculated using equation 1 as

Leq =  1mH + 2mH + 5mH = 8mH

Inductors in Series Add

Units

Inductance is measured in Henries (H). A milliHenry (mH) is one-thousandth of a  Henry. Inductors generally range in value from nanoHenries (nH) to milliHenries. An inductor in the milliHenry range is a large inductor. Because of its size, it can store a large amount of energy. The more energy an inductor can store, the more power it can generate and the higher potential of dangerous electrical shock. 

Electrical Specifications

Inductors have associated with them a resistance. They also have a rated current. The rated current should not be exceeded. For inductors in series, the inductor with the lowest rated current determines the maximum amount of current that the series circuit can safely pass. 

Applications 

Inductors are used as electronic filters, in induction motors and in transformers. They are also used extensively in power supplies. RF chip inductors are used in cell phones, local area networks and other high frequency circuits in the 10 MHz to GHz range. 

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Learning Links

Basic Facts About Inductors

Capacitors in Parallel: Electronics Tutorial # 7

When capacitors are placed in parallel, capacitors add. The equivalent capacitance of capacitors in parallel can be calculated from the formula:

Equation 1: Ceq = C1 + C2 + C3 + C4 + ..... + CN

For the circuit below, the equivalent capacitance is calculated  with equation  1 as" 

Ceq = 1uF + 2uF + 2uF + 3uF = 8uF 

Add Capacitors in Parallel to Obtain the Equivalent Capacitance

Capacitors are measured in units of Farads. A uF or microFarad, is one millionth of a Farad. For the above example, the equivalent capacitance is 8 microFarads.  

Applications 

Capacitors are often placed in parallel to increase the capacitance to a specific value that is not available as a standard component. In DC power supply application, smaller capacitors are put in parallel because smaller capacitors will filter out ripple better than one large equivalent capacitor. Parallel capacitors are often used in Kinetic Energy Conversion systems (used in electric cars). 

Limits 

Capacitors can be placed in parallel, but in practice, the total amount of voltage that can be applied across capacitor in parallel can not exceed the lowest capacitor voltage rating of the capacitors within the parallel bank. 

Learning Links 

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Capacitors in Parallel