Resistors in Series and Parallel Circuits
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Transcript Resistors in Series and Parallel Circuits
Resistors in Series and
Parallel Circuits
Resistors in circuits
To
determine the current or voltage in a
circuit that contains multiple resistors,
the total resistance must first be
calculated.
Resistors
parallel.
can be combined in series or
Resistors in Series
When
connected in series, the total
resistance (Rt) is equal to:
Rt = R1 + R2 + R3 +…
The
total resistance is always larger
than any individual resistance.
Sample Problem
Calculate the total
current through the
circuit.
15 Ω 10 Ω 6 Ω
Rt = 15 Ω +10 Ω + 6 Ω
Rt = 31 Ω
I = V/Rt = 10 V/ 31 Ω = 0.32 A
10 V
Resistors in Series
Since charge has only one path to flow
through, the current that passes through
each resistor is the same.
The sum of all potential differences equals
the potential difference across the battery.
> R value = > V Value
5V
3V
2V
10 V
Resistors in Parallel
When
connected in parallel, the total
resistance (Rt) is equal to:
1/Rt = 1/R1 + 1/R2 + 1/R3 +…
Due
to this reciprocal relationship, the
total resistance is always smaller than
any individual resistance.
Sample Problem
Calculate the total
resistance through this
segment of a circuit.
1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω
12 Ω
4Ω
= 1/12 Ω + 3/12 Ω + 2/12 Ω
1/Rt = 6/12 Ω = ½ Ω
Rt = 2 Ω
6Ω
Resistors in Parallel
Since
there is more than one possible
path, the current divides itself
according to the resistance of each
path.
smallest resistor = more current passes
largest resistor = least current passes
Resistors in Parallel
The
voltage across each resistor in a
parallel combination is the same.
10 V
10 V
10 V
10 V
Calculate the total resistance in the
circuit below
3Ω
2Ω
6Ω
4Ω
Rtot = 3 Ω + 2 Ω = 5 Ω
Rtot = 6 Ω + 4 Ω = 10 Ω
Rtot = 3 1/3 Ω
+
-
1/Rtot = 2/10 Ω+ 1/10 Ω = 3/10 Ω