Find the reactance of a
capacitor 500/π
frequency if in a
circuit a capacitor has a reactance
= 5F,
A. 2000
B. 200.50
C. 80.70
D. 190.10
The reactance of a capacitor can be calculated using the formula:
Xc = 1 / (2πfC)
where Xc is the reactance, f is the frequency, and C is the capacitance.
Given that the reactance is 5F and the capacitance is 500/π F, we can substitute these values into the formula to solve for the frequency.
5 = 1 / (2πf*(500/π))
5 = 1 / (2f*(500/π))
5 = π / (1000f)
To isolate f, we can cross multiply:
5 * 1000f = π
5000f = π
f = π / 5000
The reactance of the capacitor at this frequency is Xc = 1 / (2πfC) = 1 / (2π*(π/5000)*(500/π)) = 5000/2 = 2500 ohms
Therefore, none of the given answer choices (A, B, C, D) are correct.
To calculate the reactance (Xc) of a capacitor, you can use the formula:
Xc = 1 / (2 * π * f * C)
where Xc is the reactance of the capacitor in ohms, f is the frequency in Hertz, and C is the capacitance in farads.
Given that the capacitance is 500/π Farads and the reactance is 5 ohms, we can substitute these values into the formula and solve for the frequency (f).
5 = 1 / (2 * π * f * (500/π))
To simplify the equation, we can cancel out π from the numerator and denominator:
5 = 1 / (2 * f * (500/π))
Next, we can simplify the expression by multiplying both sides of the equation by 2f:
10f * (500/π) = 1
Further simplifying, we can divide both sides of the equation by 10(500/π):
f = 1 / (10 * (500/π))
Next, we can simplify the denominator:
f = π / (10 * 500)
Multiplying both sides of the equation by 10:
10f = π / 500
Dividing both sides of the equation by 10:
f = π / 5000
So, the frequency (f) is equal to π / 5000.
However, none of the given options match this value, so there may be an error or inconsistency in the question.