HB, MS 01212011
RC Circuits (1)
1
RC Circuits
Equipment
SWS with 750 interface, RLC circuit board, 2 voltage sensors (no alligator
clips), 2x35 in. leads, 12 in. lead
Reading
Review operation of SWS oscilloscope. Review operation of the SWS signal
generator.
1
Introduction
The 3 basic linear circuits elements are the resistor, the capacitor, and the inductor. The
voltage across a resistor is proportional to the current through the resistor. The voltage
across a capacitor is proportional to the time integral of the current into the capacitor. The
voltage across an inductor is proportional to the time derivative of the current through the
inductor. This lab is concerned with the characteristics of capacitors and circuits consisting
of a resistor and a capacitor in series (RC circuits). The primary focus will be on the response
of an RC circuit to a step voltage and a voltage square wave. (A step voltage is a constant
voltage which instantaneously changes to a diﬀerent constant voltage.)
2
Capacitors
A capacitor is a 2 terminal circuit element that stores energy in its electric ﬁeld. In its
simplest form a capacitor consists of 2 parallel plates separated by a small gap which is
usually ﬁlled with a nonconducting dielectric material. In practice many capacitors are
made by sandwiching a dielectric sheet such as mylar between 2 pieces of metal foil and
rolling this assmebly up into a cylinder.
If a positive current I enters one plate of a capacitor and exits the other plate a positive
charge Q builds up on the ﬁrst plate and a negative charge Q builds up on the second plate.
A voltage
V
C
developes across the capacitor. The charge Q and voltage
V
C
are linearly
related by the equation
Q
=
CV
C
,
(1)
where C is a constant called the capacitance. Eq. 1 can also be written as
V
C
=
1
C
Z
Idt.
(2)
The unit of capacitance in S.I. units is the farad (F). One farad is a huge capacitance and
more usual units are the micro farad (
μ
F) and the pico farad (pF). The constant C depends
on the geometry of the capacitor and the dielectric properties of the insulator between the
plates.
The most important speciﬁcation for a capacitor of a given value is its maximum voltage
rating.
3
RC Circuits
A series RC circuit with a voltage source V(t) connected across it is shown in Fig. 1. The
voltage across the resistor and capacitor are designated by
V
R
and
V
C
, and the current
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RC Circuits (1)
2
around the loop by I. The signs are chosen in the conventional way. I is positive if it is in
the direction of the arrow. Kirchoﬀ’s law, which says that the voltage changes around the
loop are zero, may be written
V
R
+
V
C
=
V.
(3)
Letting
V
R
=
IR
= (
d
dt
Q
)
R
and
V
C
=
1
C
Q
Eq.(3) may be written as
R
d
dt
Q
+
1
C
Q
=
V.
(4)
Of particular interest in this lab is the solution of Eq.(4) when
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 Spring '11
 Khurana
 RC Circuits, Square wave, Inductor, RC circuit

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