Question

C=50мкф w=5000гц l=?

Answer 1

ω=1/√(L*C)

L=1/(C*ω²)=1/(50*10^-6*25*10^12)=8*10^-8 Гн

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Answer 2

To calculate the inductance (l) in this scenario, we can use the formula for the impedance of an inductor in an AC circuit:

Z = jwL

Where: Z is the impedance (complex), j is the imaginary unit (j = √(-1)), w is the angular frequency (in radians per second), L is the inductance in henrys (H).

Given values: C = 50 μF (microfarads) w = 5000 Hz (hertz)

First, we need to convert the capacitance (C) from microfarads (μF) to farads (F) because the angular frequency (w) is given in hertz (Hz) which uses farads for capacitance. 1 μF = 1 × 10^(-6) F.

C = 50 μF = 50 × 10^(-6) F = 5 × 10^(-5) F

Now, we can calculate the inductive reactance (XL) using the formula for capacitive reactance (XC) and the relationship between them:

XC = 1 / (wC) XL = wL

Since the reactance of a capacitor and inductor cancel each other in a series combination (in resonance), we have:

XL = XC

Now, we can set the equations for the inductive and capacitive reactance equal to each other:

wL = 1 / (wC)

Now, solve for L:

L = 1 / (w^2C)

Now, plug in the values:

L = 1 / ((5000 Hz)^2 * 5 × 10^(-5) F)

L = 1 / (25,000,000 Hz^2 * 5 × 10^(-5) F)

L = 1 / (1.25 H)

L ≈ 0.8 H

So, the inductance (l) is approximately 0.8 henrys (H).