Xl = Xc = 1/6.28FC.
Xl = 1/(6.28*3681*9*10^-6) = 4.807 Ohms
Xl = 6.28FL. = 4.807.
L = 4.807 / (6.28*3681) = 0.00021 h. =0.21 mH.
My answer don't agree with any of the
given answers.
a. .000020 H
b. .000020 mH
c. .000021 uH
d. .000021 mH
Xl = 1/(6.28*3681*9*10^-6) = 4.807 Ohms
Xl = 6.28FL. = 4.807.
L = 4.807 / (6.28*3681) = 0.00021 h. =0.21 mH.
My answer don't agree with any of the
given answers.
Xc = 1 / (2Ï€fC)
Xl = 2Ï€fL
Where:
Xc is the reactance of the capacitor
Xl is the reactance of the inductor
f is the frequency of the circuit
C is the capacitance
L is the inductance
Given:
frequency, f = 3.68100017 kHz
capacitance, C = 9 uF (microfarads)
We are looking for the value of the inductance, L, when Xc and Xl have equal magnitude.
At the frequency where Xc = Xl:
1 / (2Ï€fC) = 2Ï€fL
Simplifying the equation further:
1 / (2Ï€fC) = 2Ï€fL
1 = (2Ï€fL)^2 * (2Ï€fC)
1 = L^2 * (4Ï€^2f^2) * C
Substituting the given values:
1 = L^2 * (4Ï€^2 * (3.68100017 * 10^3)^2) * (9 * 10^(-6))
Solving for L:
L^2 = 1 / ((4Ï€^2 * (3.68100017 * 10^3)^2) * (9 * 10^(-6)))
L^2 = 1 / (4.24960016176 * 10^9 * 9 * 10^(-6))
L^2 = 1 / 38.246401454784
L^2 ≈ 0.0261799
Taking the square root of both sides:
L ≈ √0.0261799
L ≈ 0.1616944
Therefore, the value of the inductor is approximately 0.1616944 H.
None of the answer choices provided match the calculated value, so there might be a mistake in the given options or in the question itself.
Xc = 1 / (2Ï€fC),
where f is the frequency in Hertz and C is the capacitance in Farads.
Similarly, the reactance of an inductor (XL) is given by the formula:
XL = 2Ï€fL,
where f is the frequency in Hertz and L is the inductance in Henrys.
In this case, we are given the frequency (3.68100017 kHz) and the capacitance (9 uF) and we need to find the inductance.
Start by converting the frequency to Hertz:
3.68100017 kHz = 3,681 Hz
Next, we'll substitute the values into the reactance formulas:
Xc = 1 / (2Ï€ * 3681 * (9 * 10^-6)),
XL = 2Ï€ * 3681 * L.
Equate the two reactances:
1 / (2Ï€ * 3681 * (9 * 10^-6)) = 2Ï€ * 3681 * L.
To solve for L, perform the following calculations:
1 / (2Ï€ * 3681 * (9 * 10^-6)) = 2Ï€ * 3681 * L.
0.00000054724053 = 2.28502618 * L.
L ≈ 0.00000054724053 / 2.28502618.
L ≈ 2.39187 * 10^-7.
The value of the inductor is approximately 0.000000239187 H, which is equivalent to 0.239187 µH.
Therefore, the correct answer is option (c) .000021 µH.