Exercises - Inductivity at AC voltage
Inductance connected to alternating voltage – exercises
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 XL?
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.
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.
- The ohmic resistance R and the inductive reactance Xbl at 50 Hz
- The inductance L
- The phase shift angle at AC voltage.
XL = 2 π f L => XL = 2 π 50s-1 0,035 H ≈ 11 Ω
XL = 2 π f L => L = XL ≈ 16,71 H
. 2 π f
R = U_ / I_ = 30 V = 12 Ω
. 2,5 A
Z = U~ = 50 V = 20 Ω
. I~ 2,5A
XL = sqrt (Z2 – R2) = sqrt (202Ω2 - 122Ω2) = 16 Ω
L = XL / 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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