Electrical and electromagnetic methods - Geophysics for the Mineral Exploration Geoscientist - page 241

a) a)

Voltage and
current in-phase

Pump

Resistance only

V alv e (open)

Water oscillates
about the same point

Phase angle

0 90° 180° 270° 360° 450° 540° 630° 720° 810° 900° 990° 1080°

Voltage Current

Core sample

b)

Resistance + capacitance

V

b)

I

Switch (closed)

Phase angle

0 90° 180° 270° 360° 450° 540° 630° 720° 810° 900° 990° 1080°

a.c. generator

Resistor

Current leads voltage

c)

e -

I

Resistance + inductance

Current oscillates
about the same point

Voltage leads current

Figure 5.4 Simple plumbing system (a) and analogous a.c. electrical
circuit (b). The oscillating piston causes the water

Phase angle

0 90° 180° 270° 360° 450° 540° 630° 720° 810° 900° 990° 1080°

flow to oscillate
about points in the system. (b) The alternating current generator
causes the charge carriers to oscillate in a similar way forming an a.c.
current. V - voltage, and I - current.

Figure 5.5 The relationship between sinusoidal variations in voltage
and current for three circuits. (a) A resistive circuit, (b) with a
capacitance and (c) with inductance.

with the variations in the applied potential, i.e. a phase shift
is introduced. Capacitance involves the energy of stored
charges and is described next. Inductance is described in
Section 5.2.2 .

under pressure as long as the pump is running, the capaci-
tor stores electrical charges on its plates, each of opposite
polarity and carrying an equal number of charges. The
uneven distribution of charges means the capacitor is
electrically polarised. The charges flow into the capacitor
from the applied potential through a process known as
charging ( Fig. 5.6d ) . Just as the volume of water confined
by the barrier is limited by the pump

5.2.1.5 Capacitance
Consider now the plumbing system in Fig. 5.6a . It contains
an elastic rubber barrier that can be deformed, but not
penetrated, by the water under pressure. Importantly, this
means the continuity of the system is interrupted, albeit
not as completely as it would be if a valve were closed.
When the pump is turned on the water

is ability to force water
against the increasing resistance presented by the barrier

'

s
elasticity, a capacitor is also limited in the amount of
charge it can store. It takes time for the capacitor to fully
charge, then the current ceases to flow in the circuit. When
the applied potential is disconnected the capacitor holds
this charge as long as the charges have no path along which
to flow. Connecting an external circuit across the capacitor
provides a current path, the charges being driven by the
mutually repulsive forces acting between the like charges
on each plate. The current flow discharges the capacitor.
The time taken for the capacitor to charge, and to dis-
charge, is dependent on the size (capacitance) of the cap-
acitor and resistance of the external circuit connected to it.
Note that the discharge current flows in the opposite
direction to the charging current ( Fig. 5.6e ) .

'

ow causes the
barrier to expand ( Fig. 5.6a ). This continues until the pump
is unable to deform the barrier any further ( Fig. 5.6b ). At
this point the water ceases to flow and there is a pressure
difference maintained across the barrier. If the pump is now
switched off the water will flow for a short time in the
opposite direction as the pressure difference dissipates
( Fig. 5.6c ) .
The electrical analogy of the elastic barrier is a capacitor,
a circuit element capable of storing electrical charge. It
comprises two conductors of large surface area, e.g. plates,
with an intervening insulator. Because the conductors are
not in electrical contact, charge can be stored on their
surfaces. Just as the water next to the barrier is maintained