Simplifying the Parallel Resistance Equation
If we have three resistors in parallel, R1, R2 and
R3:
1
1
1
1
=
+
+
Req R1 R2 R3
Applying the exponent laws:
Req
−1
−1
= R1 + R2
−1
+ R3
−1
This makes it a bit easier to manipulate the€equation. For example:
€
If R1 = 25Ω, R2 = 30Ω, and R3 = 35Ω we have:
1
1
1
1
=
+
+
Req R1 R2 R3
1
1
1
1
=
+
+
Req 25Ω 30Ω 35Ω
1
1
=
Req 9.81Ω
Req = 9.81Ω
This is just the same as:
€
Req
−1
= R1 + R2
−1
−1
Req
−1
= 25Ω−1 + 30Ω−1 + 35Ω−1
Req
−1
= 0.1019
+ R3
−1
Req = 9.81Ω
This can be done on your calculator with the reciprocal key ONLY! Try it!
€
Now, however the above was written, it is still
time consuming. That’s why you will see notation
on the Eighteen Worksheets like this:
Req = R1 || R2 || R3
€ resistance is equal to R1 in parallel with R2 in parallel
The statement simply says that the equivalent
with R3.
Req = 25Ω || 30Ω || 35Ω
And…
Req
−1
= 25Ω−1 + 30Ω−1 + 35Ω−1
(
)
Req = 25Ω−1 + 30Ω−1 + 35Ω−1
= 9.81Ω
€
−1