Download 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 =
Rt =
I = V/Rt =
10 V
Sample Problem
Calculate the total
current through the
circuit.
15 Ω 10 Ω 6 Ω
Rt = 15 Ω +10 Ω + 6 Ω
Rt =
I = V/Rt
10 V
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 =
10 V
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.
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.
12 Ω
4Ω
1/Rt =
=
6Ω
1/Rt =
Rt =
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
=
6Ω
1/Rt =
Rt =
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
6Ω
1/Rt =
Rt =
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 =
6Ω
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 =
Rtot =
Rtot =
+
1/Rtot =
-
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 =
+
1/Rtot =
-
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 =
+
-
1/Rtot = 2/10 Ω+ 1/10 Ω = 3/10 Ω
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