PASCO EM-8656 AC_DC ELECTRONICS LABORATORY - Manual (Page 47)

43
012-05892A AC/DC Electronics Laboratory
®
Experiment 13: LR Circuit
EQUIPMENT NEEDED:
– Computer and Science Workshop™ Interface
– Power Amplifier (CI-6552A)
– (2) Voltage Sensor (CI-6503)
– AC/DC Electronics Lab Board (EM-8656): inductor coil & core, 10
Ω
resistor, wire leads
– Multimeter
– (2) banana plug patch cords (such as SE-9750)
– LCR (inductance-capacitance-resistance) meter (optional)
Purpose
This experiment displays the voltages across the inductor and resistor in an inductor-resistor
circuit (LR circuit), and the current through the inductor so that the behavior of an inductor in a
DC circuit can be studied.
Theory
When a DC voltage is applied to an inductor and a resistor in series a steady current will be
established:
I
max
=
V
o
R
where V
o
is the applied voltage and R is the total resistance in the circuit. But it takes time to
establish this steady-state current because the inductor creates a back-emf in response to the rise
in current. The current will rise exponentially:
I
=
Imax(1
−
e
(R
L
)t
)
=
Imax(1
−
e
− t
t )
where L is the inductance and the quantity
L
R
= τ
is the inductive time constant. The inductive
time constant is a measure of how long it takes the current to be established. One inductive time
constant is the time it takes for the current to rise to 63% of its maximum value (or fall to 37% of
its maximum). The time for the current to rise or fall to half its maximum is related to the
inductive time constant by
t
1
2
= τ
(ln 2)
Since the voltage across a resistor is given by V
R
=
IR , the voltage across the resistor is estab-
lished exponentially:
V
R
=
V
o
(1
−
e
−
t
τ
)