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### Exercises - Inductivity at AC voltage

Inductance connected to alternating voltage – exercises

Exercise 1

An ideal coil with L = 35 mH is connected to an AC voltage with a frequency of f = 50 Hz. How big is the inductive reactance X_{L}?

Exercise 2

An ideal coil with a reactive resistance of 6.3 kΩ is connected to a frequency of 60 Hz. Determine the inductance of the coil.

Exercise 3

A real coil has an ohmic resistance (wire resistance) and a reactance. To determine these two resistances, the coil (see measuring circuit) is connected to a DC voltage of 30 V and in the following to AC voltage of 50 V / 50 Hz. The current is 2.5 A each.

Determine

- The ohmic resistance R and the inductive reactance Xbl at 50 Hz

- The inductance L

- The phase shift angle at AC voltage.

__Exercise 1:__

X_{L} = 2 π f L => X_{L} = 2 π 50s^{-1} 0,035 H ≈ __11 ____Ω__

__Exercise 2:__

X_{L} = 2 π f L => L = __ X _{L} __ ≈

__16,71__

__H__

. 2 π f

__Exercise 3:__

R = U_ / I_ = __ 30 V __ = 12 Ω

. 2,5 A

Z = __U____~__ = __ 50 V __ = 20 Ω

. I~ 2,5A

X_{L} = sqrt (Z^{2} – R^{2}) = sqrt (20^{2}Ω^{2} - 12^{2}Ω^{2}) = 16 Ω

L = X_{L} / 2 π f L = 16Ω / 2π 50s^{-1} = 50,9 mH

cos φ = R / Z = 12 Ω / 20 Ω => φ = 53,13°

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