Respuesta :
Answer:
a. The reactance of the inductor is XL = Vâ‚€/Iâ‚€
b. The inductance of the inductor is L = Vâ‚€/2Ï€fIâ‚€
Explanation:
PART A
Since the voltage across the inductor Vâ‚€ = Iâ‚€XL where Vâ‚€ = e.m.f of voltage source, Iâ‚€ = current amplitude and XL = reactance of the inductor,
XL = Vâ‚€/Iâ‚€
So, the reactance of the inductor is XL = Vâ‚€/Iâ‚€
PART B
The inductance of the inductor is gotten from XL = 2Ï€fL where f = frequency of voltage source and L = inductance of inductor
Since XL = Vâ‚€/Iâ‚€ = 2Ï€fL
Vâ‚€/Iâ‚€ = 2Ï€fL
L = Vâ‚€/2Ï€fIâ‚€
So the inductance of the inductor is L = Vâ‚€/2Ï€fIâ‚€
A) The reactance XL of the inductor : Â [tex]\frac{V_{0} }{I_{0} }[/tex] Â
B) The Inductance L of the inductor : [tex]\frac{V_{0} }{2\pi fl_{0} }[/tex] Â
A) Expressing the Reactance of the inductor
Voltage across the Inductor = Vâ‚€ = Iâ‚€XL Â ---- ( 1 )
Where : Â Vâ‚€ = emf voltage , Â Iâ‚€ = current
from equation ( 1 )
∴ XL ( reactance ) = [tex]\frac{V_{0} }{I_{0} }[/tex] Â
B ) Expressing the Inductance of the Inductor
Inductance of an inductor is expressed as : XL = 2Ï€fL
from part A
XL = [tex]\frac{V_{0} }{I_{0} }[/tex] = 2Ï€fL
∴ The inductance L of the Inductor expressed in terms of V₀, F and I₀
L = [tex]\frac{V_{0} }{2\pi fl_{0} }[/tex]
Hence we can conclude that The reactance XL of the inductor : Â [tex]\frac{V_{0} }{I_{0} }[/tex] Â and The Inductance L of the inductor : [tex]\frac{V_{0} }{2\pi fl_{0} }[/tex] Â .
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