Download Inductance - benchmark

INDUCTANCE
Benchmark Companies Inc
PO Box 473768
Aurora CO 80047
DEFINED
When a length of wire is formed onto a coil, it becomes a
basic inductor
DEFINED
Magnetic lines of force around each loop in the winding of the
coil effectively add to the lines of force around the adjoining
loops, forming a strong electromagnetic field within and
around the coil
DEFINED
A inductor is a device which stores energy in a magnetic field
DEFINED
Inductor consists of a coil of wire, usually around a metallic or
ferromagnetic core which creates an electromagnet
DEFINED
A current through an inductor creates a magnetic field around
the coil which resists any changes in current
DEFINED
The unit of inductance is the henry (H), defined as the
inductance when one ampere per Second through the coil,
induces one volt across the coil
N A
L
l
2
DEFINED
The unit of inductance is the henry (H), defined as the
inductance when one ampere per Second through the coil,
induces one volt across the coil
N 2 A
L
l
N= Number of Turns
µ = dielectric constant
A = cross-sectional area
of the coil
l = length of the coil
DEFINED
• A couple of symbols for the inductor are illustrated below
L2
L1
1.0mH
Fixed Inductor
50%
10mH-VAR
Key = A
Variable
Schematic Symbols
INDUCTOR TYPES
Toroidal core inductor
Axial Lead
Variable Inductor
Rules of Inductor Behavior

The current and voltage relationship in an
inductor is
di
i
v(t )  L  L
dt
t

If the current isn’t changing, then the
voltage change across the inductor is zero
Rules of Inductor Behavior
di
i
v(t )  L  L
dt
t
An inductor is a short circuit to DC
 The current through an inductor cannot
change instantaneously

 If
current changed quickly, then we might
have infinite voltage
 Contradicts conservation of energy
Example Problem 1
What are the values of I and V, the current through
and voltage across the inductor?

The easier value to find is the
voltage V. In this case, the
current through the inductor
isn’t changing, so the voltage
must be 0 V. So V = 0 V

In DC conditions, an inductor
acts like a short circuit – so we
need to find the current
through the resistor and it will
be the same as the current
through the inductor.
V 5V
I 
 5mA
R 1k
INDUCTOR CODE
Use the color code guide in your handout as a means to
Identify the value of the inductor.
RL TIME CONSTANT
The RL Time Constant is the time it takes, in a series
resistor inductor circuit, for current to rise to 63.2% or
fall to 36.8% of the peak voltage value of the circuit.
When five of these time constants occur, the inductor
will be fully discharged. The formula below can be used
to predict this value.
t  L/ R
t = Time in seconds
R = Resistance in Ohms
L = Inductance in Henry’s
RL TIME CONSTANT
The current across an inductor cannot change
instantaneously because a finite time is required to move
charge from one point to another (limited by circuit
resistance)
t  L/ R
t = Time in seconds
R = Resistance in Ohms
L = Inductance in Henry’s
RL TIME CONSTANT
example
With a 1kΩ resistor and a 1mH inductor are placed in
series, what is the time constant of the circuit and
how long will it take to fully discharge the inductor?
Time Constant Calculation
t =L/R
t=1mH/1kΩ
t =.001/1000
t=1us
Time for Discharge
Discharge Time = 1us x 5
Full Charge Time = 5us
RL TIME CONSTANT GRAPHIC
REPRESENTATION The first cursor proves that at
1us the current is 6.32V
The second
cursor is
showing that
after 5 time
constants the
inductor
represents a
short circuit.
THEORY
When a DC voltage source is
connected to the inductor,
voltage is maximum across the
inductor because of the
magnetic field caused by the
maximum rate of change of
current in the circuit.
Note: at t = 0 seconds
•Current is 0 Amps
•Voltage is Maximum Volts
IL  I ( t  0 )(1  e t /  )
V  Ee t / 
L
THEORY
As the magnetic field “relaxes”
due to the continuous DC,
current begins to flow through
the inductor. When this occurs,
the voltage across the inductor
begins to decrease and current
through the inductor begins to
rise.
IL  I ( t  0 )(1  e t /  )
V  Ee t / 
L
THEORY
Eventually the inductor
represents a short circuit. In an
ideal inductor the voltage drop
becomes 0 Volts and the current
through the inductor becomes
maximum.
Note: at t = infinity seconds
•Current is Maximum Amps
•Voltage is 0 Volts
IL  I ( t  0 )(1  e t /  )
V  Ee t / 
L
Series and Parallel Inductors

Inductors in Series
 With
several Inductors in series, they all act
together to affect the current
Leq  L1  L2  L3  ...  Ln
Series and Parallel Inductors

Inductors in Parallel
 With
several Inductors in parallel, we have to
split the current, just like in resistors
1
1 1 1
1
    ... 
Leq L1 L2 L3
Ln
End of Presentation