10. Reactance and Angular Velocity - Alternating Currents
by M. Bourne
An alternating current is created by rotating a coil of wire through a magnetic field. If the angular velocity of the wire is ω, the
capacitive reactance is given by:
inductive reactance is given by:
XL = ωL
If `R = 10\ Ω`, `L = 0.6\ "H"`, `C = 200\ mu "F"` and ` ω = 50\ "rad/s"`, find the magnitude of the impedance and the phase difference between the current and the voltage.
Recall: `μ` (micro) means `10^-6`.
Inductive Reactance `X_L= ωL = 50 × 0.6 = 30\ Ω`
`X_L − X_C= 30 - 100 = -70\ Ω`
`Z = 10 - 70j\ Ω` in rectangular form.
Using calculator, `|Z| = 70.71\ Ω` and ` θ = -81.87^@`.
So `Z = 70.71\ ∠\ -81.87^@\ Ω`
So the magnitude of the impedance is `70.71\ Ω` and the voltage lags the current by `81.87^@` (this is the phase difference).
Get the Daily Math Tweet!
IntMath on Twitter
Angular Velocity and Frequency
In this section, recall that angular velocity and frequency are related by the expression:
ω = 2πf