Page 838 - Mechanical Engineers' Handbook (Volume 2)

1 Basic Analog Electronics 829

Series

R R R
1 2 3

R = R + R + R + •••
effective 1 2 3

Parallel

R R R
+ V(t) – 1 2 3

1 1 1 1
= + +
R + •••
i(t) R effective R 1 R 2 R 3
Figure 4 Ideal resistor. Figure 5 Resistors.

resistors the relationship between voltage and current is linear. Linear resistors are
governed by Ohm’s law, given by V(t) i(t)R.
The magnitude of the resistance of a long cylindrical wire is related to the resistivity
of the material the wire is made of (copper and gold have low resistivity) and the length of
the wire. It is inversely related to the cross-sectional area of the wire:
(resistivity)(length)
R (2)
A cross-sectional area
Series and parallel combinations of resistors can be thought of as an effective resistance.
Resistors connected in series (share common current) create an effective resistance equal to
the sum of the resistors. Resistors connected in parallel create an effective resistance where
the inverse of the effective resistance is related to the sum of the inverse of each of the
resistors. See Fig. 5.
If there are two parallel resistors, this expression becomes
RR
R 12 (3)
E
R R 2
1
The resistance is sometimes described by the conductance G,defined as the inverse of
the resistance:
1
G (4)
R
4. Capacitor. The capacitor collects electrical charge and stores energy. The magnitude
of the capacitance is denoted C and has the units of farads (F, or coulombs per volt).
The capacitor is an energy storage element. The capacitor, like the resistor, is gov-