Capacitive Reactance Formula
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 = 1/2πfc
where,
XC is the capacitive reactance,
π 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 = 1/2πfc
= 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 = 1/2πfc
= 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 = 1/2πfc
= 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 = 1/2πfc
= 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 = 1/2πfc
=> c = 1/2πXcf
=> 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 = 1/2πfc
=> c = 1/2πXcf
=> 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 = 1/2πfc
=> f = 1/2πXcc
=> f = 1/(2 × 3.14 × 0.004 × 2)
=> f = 1/0.05024
=> f = 20 Hz
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