Data Sheet

-29-
34. Calculating Equivalent Resistance
Build the circuit, turn on the switch (62) and you will light up
the lamp (76), the star LED (70), and the bi-directional LED
(71) at the same time. Notice that the lamp (76) is dim,
but not as dim as it was in project 12. This is because the
equivalent resistance of the parallel connection of the star LED
(70) and bi-directional LED (71) is less than the resistance of
the star LED (70) alone. To prove this, assume the star LED
(70) resistance is R
star
and the bi-directional LED resistance is
R
bdled
. Then Ohm’s Law states that:
I
star
= V/R
star
AND I
bdled
= V/R
bdled
where V is the voltage across both the star LED (70) and
bi-directional LED (71), which is the same since they are
connected in parallel. Thus, the total current can be written as:
I
total
= I
star
+ I
bdled
= V/R
star
+ V/R
bdled
= (V*R
bdled
+ V*R
star
) / R
star
*R
bdled
= V*(R
bdled
+ R
star
) / R
star
*R
bdled
Solving for V yields: V = I
total
*R
star
*R
bdled
/ (R
bdled
+ R
star
)
This shows that the equivalent resistance through the parallel
connection of the star LED (70) and bi-directional LED (71) is
R
star
*R
bdled
/(R
bdled
+ R
star
). If for simplicity we were to assume
that the internal resistance of the star LED (70) is the same as
the internal resistance of the bi-directional LED (71), and thus
R
star
= R
bdled
= R, then the equivalent resistance of the parallel
connection is R*R/(R+R) = R/2. Thus the equivalent resistance
of the parallel connection is half that compared to having the
resistance from just the star LED (70) in the circuit (like in project
12), which is why the lamp (78) is not as dim in this project.