Data Sheet

-42-
53. Calculating Equivalent Resistance
Build the circuit shown on the left and you will see the motor (95) spin
and the two LEDs turn on at the same time. It is interesting that the
motor (95) spins in this circuit but does not spin or at least slows
down if you remove the star LED (70) from the circuit. This is because
the equivalent resistance of the two LEDs in parallel is less than the
resistance of either one alone. To prove this, assume the star LED
(70) resistance is R
star
and the heart LED (69) resistance is R
heart
. Then
Ohm’s Law states that:
I
star
= V/R
star
and I
heart
= V/R
heart
where V is the voltage across both the star LED (70) and heart LED
(69), which is the same since they are connected in parallel. Thus, the
total current can be written as:
I
tot
= I
star
+ I
heart
= V/R
star
+ V/R
heart
= (V*R
heart
+ V*R
star
) ÷ R
star
*R
heart
= V*(R
heart
+ R
star
)/R
star
*R
heart
Solving for V yields:
V = I
tot
*R
star
*R
heart
/(R
heart
+ R
star
)
This shows that the equivalent resistance through the parallel connection
of the star LED (70) and heart LED (69) is R
star
*R
heart
/(R
heart
+ 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 heart LED (69),
and thus R
star
= R
heart
= 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 heart LED (69) in the circuit, which is why the motor (95)
spins in this project.
1st level 1st level
+
–