Question
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
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
Answers
Answered by
GPT 3.5
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.
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.