Exercice
1
Determine how v
changes when i
is (a) doubled, and (b) halved.
Type your answer in the box below:
Solution: Apply Ohm’s
law
(a) V
(2 i)
= 2 i
R
= 2 V(i),
v
is doubled when i
is doubled.
(b) V
(i/2)
= i
R/2
= 1/2 V(i),
v
is halved when i
is halved.
We see that the change in i
produces the same change in v.
This means that v
varies directly with the variation of
i.
This behavior is called direct variation.
Graphing a Linear Equation
What is a
Graph?
A graph is a representation of the
relationship between two or more quantities.
What is a Linear Equation?
It is an equation whose solution is
a straight line. A linear equation has
the general form
where
y
= dependent variable
m
= coefficient of x
x
= independent variable
b
= a constant
Why do we
use graphs?
The objective of the graph is to interpret
an electric circuit condition from
the information seen in the graph.
Figure 5.2
Graph with horizontal and vertical
axes of a rectangular coordinate system
-
The horizontal axis (x-axis)
represents the values of voltage
while the vertical axis (y-axis)
represents the values of current.
-
The x-axis
and y-axis
intersect at the origin. Pair
of numbers called coordinates
indicates each point on the graph.
-
Usually, the independent variable
is assigned to the x-coordinate
(i.e., v),
and the dependent variable is
assigned to the y-coordinate (i.e.,
i).
-
The coordinates of the points
in a plane may be negative or
positive depending upon the quadrant
in which they are located.
-
A solution of the graph represents
an equation.
-
The coordinates of any point
on the graph satisfy the conditions
of the equation.
-
The graph in Figure 5.2 represents
a straight line (i.e., linear
equation).
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