Page 837 - Mechanical Engineers' Handbook (Volume 2)

828 Mechatronics

2. Voltage. Voltage is the electromotive force or potential difference and is designated
with the symbol V (or e, E, v). It is a measure of the potential of an electric field.
The electrical voltage has the units of volts and is generally written
potential of A with respect to B
V AB
or more commonly with a (plus sign) at point A and a (minus sign) at point B.
3. Power. Power is defined as the ability to do work. The flow of power is generally
what is described by engineering models. Power has units of watts and is the product
of the voltage and current.
4. Work. Work (or energy) has units of joules and is the integral of power over time:

t ƒ
W P(t) t (1)
t 0

1.2 Basic Electrical Elements
Several elements and their constitutive relationships need to be understood to analyze basic
electrical circuits. The constitutive relationship for each element describes the relationship
between the voltage (effort variable) and the current (flow variable):
1. Ideal Voltage Source. The ideal voltage source produces a voltage, or electrical po-
tential, as a function of time. This voltage produced by the source is an input to the
system and the voltage source adds power to the system. The current passing through
the ideal voltage source is not generally known. This current is determined by the
other elements connected to the voltage source. The ideal voltage source is capable
of producing infinite current and therefore infinite power. See Fig. 2.
2. Ideal Current Source. The ideal current source produces a current as a function of
time. This current produced by the source is an input to the system and the current
source adds power to the system. The voltage across the ideal current source is not
generally known. This voltage is determined by the other elements connected to the
current source. The ideal current source is capable of producing infinite voltage and
therefore infinite power. See Fig. 3.
3. Resistor. The resistor restricts the flow of current and dissipates power. The magnitude
of this resistance is denoted R and has the units of ohms ( ). The resistor is a passive
element in that it does not add energy to the system. The resistor is governed by a
passive sign convention, as shown in Fig. 4, in that the current flows across the
resistor from the side of higher potential (voltage) to the side of lower potential
(voltage). If the current and the voltage are negative, this indicates that current flow
is in the opposite direction and the potential is higher on the opposite side. In linear

+
V(t) I(t)

–

Figure 2 Ideal voltage source. Figure 3 Ideal current source.