Inductance
Inductance opposes a change in current.
Inductors create a voltage that opposes the current.
Counter EMF(voltage)
Lv
Inductance
The Henry (symbol: H) is the SI unit of inductance.
It is named after the American physicist Joseph Henry..
E L IVoltage InductanceInductance CurrenCurren
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Voltage leads CurrentVoltage leads Current
in anin an
Inductive CircuitInductive Circuit
Current Voltage
I = Ipsin(2πft) Ip-Peak Current
2π-Cycle
f-frequency(Hz)
t-time(seconds)
V = L di/dt
V = L Ip(2πf)cos(2πft)
Vp = Ip(2πf)L
V = L d(Ipsin(2πft))/dt
Calculate the maximum current in a coil which has an inductance of 3 mH. The frequency is 60Hz. The maximum voltage across the coil is 6 V.
XL = 2πfL
L=3mH E=6Vf=60Hz
XL = 2π(60Hz)(.003H)
XL = 1.13Ω
I = E/XL
I = 6V/1.13Ω
I = 5.3A
Inductive/Resistive Circuit 90° Phase Shift caused by Inductor Impedance, Z, is calculated by
adding XL and R vectorially.
XL
R
Z
What is the impedance of a 100mH choke in series with a 470Ω resistor with a 12V, 60Hz applied across them? What is the phase angle between voltage and current?
XL = 2πfL
L=100mH E=12Vf=60Hz
XL = 2π(60Hz)(.1H)
XL = 37.7Ω
R=470Ω
Xc = 1/(2πfC)
Xc = 1/(2π(60)(1.5X10-6)
Xc = 1768Ω
XL = 2πfL
XL = 2π(60)(0.65)
XL = 245Ω
XL
RZXC
𝚹 = -81°ICE – Current leads Voltage by 81°
Resonance The frequency where XL = XC
The Circuit becomes a purely resistive circuit
Xc = 1/(2πfC) XL = 2πfL
1/(2πfC) = 2πfL
Xc = XL
1/(4π2CL) = f2
= f