The graph of a straight line represents a proportional relationship between input variables and output values; with every increase ( or decrease ) in input values, a proportionate change in output can be expected. The graph of a straight line can be graphed via usage of the following formula:
y = mx + b
For the sake of simplicity, we may assume ( b ) to have a value of zero, and thus:
y = mx
And,
( y / x ) = m = constant
As can be seen, a line with a greater slope has larger output values per input value than lines with a smaller slope. This is analogous to a higher voltage ( V2 ) giving rise to a higher current ( I2 ) across a resistor ( R ) than a current ( I1 ) induced by a lower voltage ( V1 ) across the same resistor:
V = IR
( V / R ) = I
( V2 / R ) > ( V1 / R )
I2 > I1
Ohm’s Law explicitly states that a current produced by a system is directly proportional to voltage and inversely proportional to resistance. Fortunately, a relatively simple visual aid can be used to ascertain how V, I, and R are related to one-another. We first draw a circle that is split into two parts by a horizontal diameter. Next, we subdivide the lower half of the circle with a vertically oriented radius. This leaves us with a larger space in which we place ( V ) and two smaller sections within which we place the ( I ) and ( R ):
The horizontally oriented diameter represents division, and the vertically oriented radius represents multiplication. If we cover the V and R, we are left with I. Likewise, covering V and I leaves us with R, and covering I and R leaves us with V.
RENAISSANCE PHYSICS 