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Capacitive Reactance Formula

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Capacitive Reactance is the measurement of a capacitor’s resistance to alternating current. It is known that a capacitor is defined as a device that stores current and has the ability to influence the amount of charging it can achieve. The value of its capacitance is determined by the frequency f of the electrical signal travelling through it. It is the resistance of a circuit element to changes in current or voltage. Its standard unit of measurement ohms (Ω). It is represented by the symbol Xc and its dimensional formula is given by [M1L2T-3I-2]. Its mathematical formula is equal to unity divided by twice the product of pi, frequency and the capacitance of a capacitor.

Capacitive Reactance Formula

Xc = 1/2Ï€fc

where,

XC is the capacitive reactance,

Ï€ is a constant with the value of 3.14,

f is the frequency,

c is the capacitance.

Sample Problems

Problem 1. Find the capacitive reactance if the capacitance is 5 F for a frequency of 20 Hz.

Solution:

We have,

f = 20

c = 5

Using the formula we have,

Xc = 1/2Ï€fc

= 1/(2 × 3.14 × 20 × 5)

= 1/628

= 0.0016 Ω

Problem 2. Find the capacitive reactance if the capacitance is 4 F for a frequency of 50 Hz.

Solution:

We have,

f = 50

c = 4

Using the formula we have,

Xc = 1/2Ï€fc

= 1/(2 × 3.14 × 50 × 4)

= 1/2512

= 0.00039 Ω

Problem 3. Find the capacitive reactance if the capacitance is 0.5 F for a time of 10 s.

Solution:

We have,

t = 10

c = 0.5

Using the formula f = 1/t we get,

f = 1/10

= 0.1 Hz

Using the formula we have,

Xc = 1/2Ï€fc

= 1/(2 × 3.14 × 0.1 × 0.5)

= 1/0.314

= 3.183 Ω

Problem 4. Find the capacitive reactance if the capacitance is 2.5 F for a time of 16 s.

Solution:

We have,

t = 16

c = 2.5

Using the formula f = 1/t we get,

f = 1/16

= 0.0625 Hz

Using the formula we have,

Xc = 1/2Ï€fc

= 1/(2 × 3.14 × 0.0625 × 2.5)

= 1/0.98125

= 1.0186 Ω

Problem 5. Find the capacitance, if capacitive reactance is 2 Ω for a frequency of 25 Hz.

Solution:

We have,

Xc = 2

f = 25

Using the formula we have,

Xc = 1/2Ï€fc

=> c = 1/2Ï€Xcf

=> c = 1/(2 × 3.14 × 2 × 25)

=> c = 1/314

=> c = 0.003183 F

Problem 6. Find the capacitance, if capacitive reactance is 0.01 Ω for a frequency of 12 Hz.

Solution:

We have,

Xc = 0.01

f = 12

Using the formula we have,

Xc = 1/2Ï€fc

=> c = 1/2Ï€Xcf

=> c = 1/(2 × 3.14 × 0.01 × 12)

=> c = 1/0.7536

=> c = 1.327 F

Problem 7. Find the frequency if capacitive reactance is 0.004 Ω for the capacitance of 2 F.

Solution:

We have,

Xc = 0.004

c = 2

Using the formula we have,

Xc = 1/2Ï€fc

=> f = 1/2Ï€Xcc

=> f = 1/(2 × 3.14 × 0.004 × 2)

=> f = 1/0.05024

=> f = 20 Hz


Last Updated : 04 Feb, 2024
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