# Capacitive Voltage Divider (2023)

Outline

### Introduction

In a voltage divider circuit,the supply voltage or circuit voltage is distributed among all the components in the circuit equally,depending on the capacity of those components.

The construction of capacitive voltage divider circuit is same as like resistive voltage divider circuit. But like resistors, the capacitive voltage divider circuit is not affected by the changes in the frequency even though it uses reactive elements.

The capacitor is a passive component which stores electrical energy in the metal plates. A capacitor has two plates and these two are separated by non-conducting or insulating material, such as called as “dielectric”.

Here the positive charge is stored on one plate and negative charge is stored on another plate.

When DC current is applied to the capacitor, it charges fully. The dielectric material between the plates acts as insulator and also it opposes the current flow through the capacitor.

This opposition to supply current through the capacitor is called reactance (XC) of a capacitor. The capacitor reactance is also measured in ohms.

A fully charged capacitor acts as an energy source, because a capacitor stores energy and discharges it to the circuit components.

If an AC current is applied to the capacitor then the capacitor continuously charges and discharges the current through its plates.In this time the capacitor also has reactance which varies depends on supply frequency.

We know that the charge which is stored in the capacitor depends on the supply voltage and the capacitance of a capacitor.

In the same way the reactance also depends on some parameters, now we see the parameters which influence the reactance of a capacitor.

(Video) Capacitive Voltage Divider

If a capacitor has smaller capacitance value , then the time required to charge a capacitor is less , i.e. smaller RC time constant is required. In the same way the RC time constant is high for larger capacitance value of capacitors.

From this we observed that , larger capacitance value capacitor has less reactance value where as smaller capacitance value of capacitor has larger reactance value. i.e. the reactance of a capacitor is inversely proportional to the capacitance value of the capacitor.

XC∝ 1/C

If the frequency of applied current is low then the charging time of capacitor increases,it indicates that reactance value is high. In the same way if the frequency of applied current is at high, then the reactance of the capacitor is low.

From this we can observe that the reactance of a capacitor is inversely proportional to the frequency.

Finally, we can say that, the reactance (XC) of any capacitor is inversely proportional to the frequency (f) and the capacitance value (C).

XC∝ 1/f

### Capacitive Reactance Formula

Already we know that the capacitive reactance is inversely proportional to the frequency and capacitance value of the capacitor. Thus formula for reactance is

XC = 1/2πfC

Here,

XC = Reactance of a capacitor in ohms (Ω)

f = Frequency in Hertz’s (HZ)

C = Capacitance of a capacitor in Farads (F)

π = Numeric constant (22/7 = 3.142)

(Video) Capacitive Voltage Dividers

### Voltage Distribution in Series Capacitors

If the capacitors are connected in series , the voltage distribution between the capacitors is calculated. Because the capacitors have different voltage values depending on the capacitance values in series connection.

The reactance of a capacitor which opposes the flow of current , depends on the value of capacitance and frequency of the applied current.

So now let us see how the reactance affects the capacitors , by calculating the frequency and capacitance values. Below circuit shows the capacitive voltage divider circuit in which 2 capacitors are connected in series.

### Capacitive Voltage Divider The two capacitors which are connected in series have the capacitance values of 10uF and 22uF respectively. Here the circuit voltage is 10V,this voltage is distributed between both capacitors.

In the series connection all the capacitors have same charge (Q) on it but the supply voltage (VS) is not same for all capacitors.

The circuit voltage is shared by the capacitors depending on the capacitance values of the capacitors.i.e. in the ratio of V = Q/C.

From these values we have to calculate the reactance (XC) of each capacitor by using frequency and capacitance values of capacitors.

### Capacitive Voltage Divider Example No1

Now we will calculate the voltage distribution to the capacitors 10uF and 22uF which are given in the above figure which have 10V supply voltage with 40HZ frequency.

Reactance of 10uF capacitor,

XC1 = 1/2πfC1 = 1/(2*3.142*40*10*10-6) = 400Ω

Reactance of 22uF capacitor,

XC\2 = 1/2πfC2 = 1/(2*3.142*40*22*10-6) = 180Ω

(Video) Electrical Engineering: Ch 6: Capacitors (19 of 26) Capacitors as Voltage & Current Dividers

Total capacitive reactance of a circuit is,

XC= XC1+ XC2= 400Ω + 180Ω = 580Ω

CT= C1C2/(C1+C2) = (10*22*10-12)/(32*10-6) = 6.88uF

XCT = 1/2πfCT = 1/(2*3.142*40*6.88*10-6) = 580Ω

The current in the circuit is,

I = V/XC = 10V/580Ω = 17.2mA

Now, the voltage drop across each capacitor is,

VC1 = I*XC1 = 17.2mA*400Ω = 6.9V

VC2 = I*XC2 =17.2mA*180Ω = 3.1V

### Capacitive Voltage Divider Example No2

Now we calculate the voltage drops across the capacitors 10uF and 22uF which are connected in series and they operate with 10V supply voltage of 4000HZ (4KHZ) frequency.

Reactance of 10uF capacitor,

XC1 = 1/2πfC1 = 1/(2*3.142*4000*10*10-6) = 4Ω

Reactance of 22uF capacitor,

XC\2 = 1/2πfC2 = 1/(2*3.142*4000*22*10-6) = 1.8Ω

(Video) ENGR 313 - 04.04 Capacitive Voltage Divider Circuit Example

Total capacitive reactance of a circuit is,

XC= XC1+ XC2 = 4Ω+1.8Ω = 5.8Ω

CT = C1C2/(C1+C2) = (10*22*10-12)/(32*10-6) = 6.88uF

XCT = 1/2πfCT = 1/(2*3.142*4000*6.88*10-6) = 5.8Ω

The current in the circuit is,

I = V/XCT = 10V/5.8Ω = 1.72A

Now, the voltage drop across each capacitor is,

VC1 = I*XC1 = 1.72A*4Ω = 6.9V

VC2 = I*XC2 = 1.72A*1.8Ω = 3.1V

From the above two examples we can concludethat the lower value capacitor (10uF) will charge to a higher voltage (6.9V), and the higher value capacitor (22uF) will charge itself to a lower voltage level(3.1V).

Finally the sum of two capacitor voltage drops values are equal to the supply voltage (i.e. 6.9V+3.1V=10V). These voltage values are same for all frequency values, because the voltage drop is independent of frequency.

The voltage drops for the two capacitors is same in both the examples where the frequency is different. The frequency is either 40HZ or 40KHZ the voltage drops across capacitors is same in both cases.

The current flowing through the circuit changes depending on the frequency. Current will increase with increasing the frequency, it is 17.2mA for 40HZ frequency but it is 1.72A for the frequency 4KHZ, i.e. the current will increase almost 100 times by increasing frequency 4HZ to 4KHZ.

Finally we can saythat the current flowing through the circuit is directly proportional to the frequency (I α f).

(Video) Capacitive Voltage Divider

### Summary

• The opposition for the flow of current in the capacitor is known as reactance (XC) of a capacitor. This capacitive reactance is influenced by the parameters like capacitance value,frequency of supply voltage and also these values are inversely proportional to the reactance.
• The AC voltage divider circuit will distribute the supply voltage to all the capacitors depending on their capacitance value.
• These voltage drops for the capacitors are same for any frequency of supply voltage. i.e. the voltage drops across capacitors are independent on frequency.
• But the current flowing is depending on frequency and also these two are directly proportional to each other.
• But in DC voltage divider circuits, it is not an easy task to calculate the voltage drops across capacitors as it depends on reactance value, because the capacitors block DC current flow through it after fully charged.
• The capacitive voltage divider circuits are used in large electronics applications.Mainly used in capacitive sensitive screens those change their output voltage when it is touched by a person finger.
• And also used in transformers to increase voltage drop where generally the mains transformer contains low voltage drop chips and components.
• Finally one thing to say is in voltage divider circuit the voltage drops across capacitors are same for all frequency values.

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## FAQs

### How do you calculate capacitive voltage divider? ›

Capacitive DC Voltage Divider Circuit

Voltage is divided up in a capacitive DC voltage divider according to the formula, V=Q/C. Therefore, voltage is inversely proportional to the capacitance value of the capacitor.

Why capacitance voltage dividers are not preferred for high DC voltage measurements? ›

As capacitive voltage dividers use the capacitive reactance value of a capacitor to determine the actual voltage drop, they can only be used on frequency driven supplies and as such do not work as DC voltage dividers. This is mainly due to the fact that capacitors block DC and therefore no current flows.

Can you do a voltage divider with capacitor? ›

Similar to resistors, capacitors can also be used to form a voltage divider circuit so that voltage can be separated into parts of a circuit based on the capacitor value. Similar to a voltage divider circuit using resistors, capacitors are connected in series to form a voltage divider network with a voltage source.

What is the 10 percent rule for voltage dividers? ›

Voltage Divider and the 10% Rule

The voltage divider should only have a 10% bleeder current– the current drawn continuously from a voltage source to lessen the effect of load changes or to provide a voltage drop across a resistor.

What is the formula for capacitive calculation? ›

This calculates the capacitance of a capacitor based on its charge, Q, and its voltage, V, according to the formula, C=Q/V.

How do you solve capacitive? ›

To calculate the total overall capacitance of a number of capacitors connected in this way you add up the individual capacitances using the following formula: CTotal = C1 + C2 + C3 and so on Example: To calculate the total capacitance for these three capacitors in parallel.

Why are voltage dividers bad? ›

It wastes ALL the battery's power. A series resistance wastes power. A series resistance and a resistance to ground (in a voltage divider) has both resistors wasting power. A series resistor and a voltage divider produce very poor voltage regulation.

What are the cons of voltage dividers? ›

Voltage Dividers Cons:
• Not very stable.
• Not very rigid.
• Unnecessary or excessive power dissipation.
• Plenty of other option.
Jan 18, 2019

Why add capacitor to voltage divider? ›

Additionally, if the input impedance has capacitive elements, using a completely resistive divider will unintentionally create an RC filter, which can limit the data rate. Adding a capacitor in series with the top resistor (making both legs of the divider capacitive and resistive) can help overcome this.

Why are the capacitive voltage divider preferred for high AC voltage measurements? ›

This ensures that the current cannot pass from the high voltage circuit to the delay cable without actually going through the foil electrodes. It is also important that the coupling between the high and low voltage arms of the divider be purely capacitive.

### Does the voltage increase when capacitor plates are separated? ›

If the capacitor has a constant charge, changing the capacitance should cause the voltage to vary. Moving the plates apart will reduce the capacitance, so the voltage should increase.

Can a capacitor block DC voltage? ›

As soon as the power source fully charges the capacitor, DC current no longer flows through it. Because the capacitor's electrode plates are separated by an insulator (air or a dielectric), no DC current can flow unless the insulation disintegrates. In other words, a capacitor blocks DC current.

What is a perfect voltage divider? ›

An ideal voltage divider is just two resistors in series. Physically, this is occasionally implemented as a potentiometer, which splits a single physical resistor in two with a physically moveable conductive center contact. But most often, it's two discrete fixed resistors.

What should voltage dividers not be used to do? ›

Application Dont's

As tempting as it may be to use a voltage divider to step down, say, a 12V power supply to 5V, voltage dividers should not be used to supply power to a load. Any current that the load requires is also going to have to run through R1.

Do voltage dividers reduce current? ›

After connected the load resistor, the voltage divider circuit turned into a series-parallel circuit. Therefore, the total resistance of the circuit is reduced. The circuit current increases because the total resistance of the circuit is decreased.

What are the three methods of calculating capacitance? ›

Three different measurement methods, or variants thereof, are often employed to find the capacitance; galvanostatic charging, cyclic voltammetry and impedance spectroscopy.

How do you calculate capacitance from voltage and current? ›

Capacitance (C) = charge (Q) / volts (V). The size of a capacitor (C) is specified in terms of the ratio of the charge it holds (Q) to the voltage across it (V). The unit of capacitance (C) is the farad (F).

Can current flow through a capacitor? ›

Even though a capacitor has an internal insulator, and that's going to be right here, current can flow through the external circuit as long as the capacitor is charging and discharging, so as long as it's charging and discharging current can flow.

How do you solve capacitance examples? ›

• μF = Q/40. Q = 40 μC. Find the charge on the 2 μF capacitor: C = Q/V.
• μF = Q/40. Q = 80 μC. Find the charge on the 3 μF capacitors: C = Q/V.
• μF = Q/40.

What is the formula for capacitance work done? ›

q=CV. We know that W = V q , W=Vq, W=Vq, i.e. work done is equivalent to the product of the potential and charge.

### How accurate is voltage divider? ›

The actual output of the voltage divider is low by 4% compared to the target voltage. Notice the 4% voltage error is significantly less than the 9% change of resistance.

Does current matter in a voltage divider? ›

Does a voltage divider limit current? Not really. The voltage divider does not limit the current, only change the high voltage to the low voltage.

Why is voltage divider most stable? ›

1 Answer. The operating point does not depend upon the value of β of the transistor. Hence the operating point does not change its position due to rise in temperature or replacing a transistor of different p value. Hence voltage divider bias provides excellent stabilisation and is preferred to other biasing methods.

Does voltage divider affect frequency? ›

Voltage dividers can be constructed from reactive components just as they can be constructed from resistors. Also, as with resistor dividers, the divider ratio of a capacitive voltage divider is not affected by changes in the signal frequency even though the capacitor reactance is frequency dependent.

Does voltage divider work for more than 2 resistors? ›

VRx=Vin(RxRT) V R x = V i n ( R x R T ) . In this equation, the output voltage is the voltage drop across the specific resistor x. Rx is the value of the specific resistor, and RT is the total resistance of the circuit. In this way, a circuit can have as many resistors as needed in a voltage divider circuit.

Why is voltage divider bias better? ›

Voltage divider bias will give better stability compared to all other circuits (fixed bias, collector feedback bias). Note: The goal of transistor biasing is to establish a known quiescent operating point or Q-point for the bipolar transistor to work efficiently and produce an undistorted output signal.

Does capacitor improve voltage? ›

Capacitors are used to store electrical energy, although they cannot increase the voltage on their own. The voltage multiplier circuit is made by connecting a capacitor and a diode. In many circuits where the output voltage must be greater than the input voltage, capacitors can be used.

Does a capacitor reduce voltage? ›

The voltage drop across a capacitor is proportional to its charge, and it is uncharged at the beginning; whereas the voltage across the resistor is proportinal to the current and there is a current at the start. But charge starts to build up on the capacitor, so some voltage is dropped across the capacitor now.

Why do you need a capacitor with a voltage regulator? ›

In a voltage regulator, capacitors are placed at the input and output terminals, between those pins and ground (GND). These capacitors' primary functions are to filter out AC noise, suppress rapid voltage changes, and improve feedback loop characteristics.

Does higher capacitance mean higher voltage? ›

Here, from the equation, it is clear that capacitance is inversely proportional to voltage. So, when voltage increases capacitance decreases, and when the voltage decreases, capacitance increases.

### What happens when an AC voltage is applied to a purely capacitive circuit? ›

The phrase “applied to a pure capacitor” signifies that there are no resistive elements or inductive elements in the circuit. Now, in such cases when ac voltage is applied to a capacitor, during the first cycle as the ac voltage increases, current flows into the capacitor.

How to reduce AC voltage using capacitor? ›

To reduce the 220V AC, an X-rated capacitor of 0.1 uF 400 V rating is used in series with the phase line. The resistor R1 of 200 k ohms and 1 W power rating is connected parallel with the capacitor. The resistor R1 is a bleeder resistor which is used for safety purpose.

What happens to a capacitor if too much voltage is supplied to the plates? ›

If the voltage applied across the capacitor becomes too great, the dielectric will break down (known as electrical breakdown) and arcing will occur between the capacitor plates resulting in a short-circuit.

Why does voltage decrease when capacitance increases? ›

This comes from the fact that C=ε*A/d where ε is the permittivity of the dielectric. The capacitance increases but the charge has nowhere to go, thus causing the voltage to decrease.

What happens when a capacitor is over voltage? ›

Maximum voltage - Each capacitor is rated for a maximum voltage that can be dropped across it. Some capacitors might be rated for 1.5V, others might be rated for 100V. Exceeding the maximum voltage will usually result in destroying the capacitor.

What happens if we connect capacitor to DC? ›

Capacitors can be used as temporary storage devices after being connected to DC voltage. Once fully charged the capacitors will stop allowing any more electrons to reach the plates. Thus the capacitor stops the DC once it is fully charged.

What happens if we apply DC to capacitor? ›

When a DC voltage is applied across a capacitor, a charging current will flow until the capacitor is fully charged when the current is stopped. This charging process will take place in a very short time, a fraction of a second. Hence, a fully charged capacitor blocks the flow of DC current.

Can AC current pass through capacitor? ›

Capacitor blocks direct current but easily passes alternating current.

What is the rule of thumb for voltage divider? ›

The rule of thumb is: the source impedance should be about ten times less than the load impedance. For the best transfer of voltage from source to load, you may want to make this ratio even higher. A source impedance 100x less than the load will maintain nearly all of the source voltage.

How can I improve my voltage divider? ›

Higher divider current = lower noise.
...
There are several things that can be done to improve the accuracy of your measurements:
1. Try using more of the full scale range of the ADC. ...
2. Use resistors with tighter tolerances (try 0.1% or better) and better specifications for temperature drift.
Aug 10, 2021

### What is the simplest type of voltage divider? ›

Resistive Voltage Dividers

The simplest, easiest to understand, and most basic form of a passive voltage divider network is that of two resistors connected together in series. This basic combination allows us to use the Voltage Divider Rule to calculate the voltage drops across each series resistor.

What is the 10% rule for voltage dividers? ›

Voltage Divider and the 10% Rule

The voltage divider should only have a 10% bleeder current– the current drawn continuously from a voltage source to lessen the effect of load changes or to provide a voltage drop across a resistor.

What is the formula for a capacitor voltage divider? ›

Capacitive AC Voltage Divider Circuit

The formula XC= 1/ (2πfc) guides voltage division through individual capacitors in a capacitive voltage divider circuit. Even so, to calculate the amount of voltage allocated to the circuit's capacitors, you need first to calculate the capacitor's impedance.

What is the most efficient way to reduce voltage? ›

The simplest way to reduce voltage drop is to increase the diameter of the conductor between the source and the load, which lowers the overall resistance. In power distribution systems, a given amount of power can be transmitted with less voltage drop if a higher voltage is used.

Can capacitors be used as voltage dividers? ›

Similar to resistors, capacitors can also be used to form a voltage divider circuit so that voltage can be separated into parts of a circuit based on the capacitor value. Similar to a voltage divider circuit using resistors, capacitors are connected in series to form a voltage divider network with a voltage source.

What is the formula of voltage divider formula? ›

The voltage divider formula for a circuit with multiple resistors is VRx=Vin(RxRT) V R x = V i n ( R x R T ) where Rx is the specific resistor across which the output voltage drop is being measured. This is the ratio of the resistor value to the total resistance of the circuit multiplied by the input voltage.

What is the formula for the current divider of a capacitor? ›

The equation for the current divider formula is I_2=I_Total*Z_1/(Z_1+Z_2 ). Collectively, for the parallel circuit is “total current multiplied by (ratio of the impedance of the opposite resistor divided by impedance sum).

What is the formula for capacitive impedance? ›

When converting the impedance of a capacitor, we use the formula Z = -jX.

What is the formula for voltage divider for RC? ›

The divider ratio V 2/ V S = XC2/(XC1+XC2). The capacitive reactance XC is proportional to 1/C so V 2/ V S = C1/(C1+C2) is similar to the formula for the resistor divider.

What is the math for voltage divider? ›

The Voltage Divider Method is a formula we can utilize as a shortcut to Ohm's Law ( V = I R ) (V=IR) (V=IR) in certain cases—when the electric circuit question is asking for voltage and/or resistance, it is no longer necessary to solve for the electric current before calculating the voltage across center resistors.

### What is the voltage divider rule easy? ›

The voltage division rule states that the voltage across any of the series components in a series circuit is equal to the product of value of that resistance and the total supply voltage, divided by the total resistance of the series circuit.

What is the use of capacitive voltage divider? ›

Capacitive voltage dividers are often also used to measure high voltages. Capacitive voltage dividers determine the voltage drop based on the reactance of the capacitor network, and as such, do not work as DC voltage dividers. After all, capacitors block DC and result in no current flow.

What are the formulas for capacitive reactance? ›

Capacitive reactance is defined as:(10-1)Xc=1/ωC=1/2πfCwhere XC is the capacitive reactance, ω is the angular frequency, f is the frequency in Hertz, and C is the capacitance.

How do you find capacitance from resistance? ›

The resistance considers the equation Vout(t)=V(1−e−t/τ), where τ=RC. The capacitance, output voltage, and voltage of the battery are given. We need to solve this equation for the resistance.

What is the formula for capacitor impedance vs frequency? ›

Answer: The capacitance impedance calculator calculates the impedance of a capacitor based on the value of the capacitance, C, of the capacitor and the frequency, f, of the signal passing through the capacitor, according to the formula, XC=1/(2πfC).

Where is voltage divider formula used? ›

Voltage dividers are used for adjusting the level of a signal, for bias of active devices in amplifiers, and for measurement of voltages. A Wheatstone bridge and a multimeter both include voltage dividers. A potentiometer is used as a variable voltage divider in the volume control of many radios.

What is a voltage divider between two voltages? ›

A voltage divider is a simple circuit which turns a large voltage into a smaller one. Using just two series resistors and an input voltage, we can create an output voltage that is a fraction of the input. Voltage dividers are one of the most fundamental circuits in electronics.

## Videos

1. CVT:Capacitor Voltage Transformer:Potential Divider:CVT working Principle
(Electrical Passionate)
2. A talk about the capacitive voltage divider on AC (alternating current)
3. Capacitance potential divider & Capacitance voltage transformer
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4. The Capacitive Voltage Divider Illustrated Using a MOS Capacitor, Lecture 69
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5. Introduction to Capacitive Voltage Transformer | Video #3
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6. Capacitive Voltage Transformer|CVT|Capacitive Voltage Divider Transformer
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