Parallel Circuits - Southern Illinois University Carbondale
ET 150
In this presentation you will learn: how to recognize a parallel circuit the characteristics of a parallel electric circuit how to find the currents flowing in each branch of a parallel circuit using Ohm's Law how to find the total current flowing in a parallel circuit how to compute the equivalent resistance of a group of parallel loads
V1
V2
V3
Characteristics
Loads connected "across" voltage
Is
source
Es
I1
R1 I2
R2 I3
(Each load has connections to R3 terminals of voltage source)
Voltage the same across each load.
Is = I1 + I2 +I3
Current divides among loads based on load resistance (smaller R greater I)
Commonly used in house wiring
Sum of load currents equals source current (Kirchhoff's Current Law)
V1
V2
V3
Is
I1
I2
I3
R1
R2
R3
Es
Solving Parallel Circuits Using Ohm's Law
V1 =V2 =V3 =Es
I1
=
Es R1
I2
=
Es R2
I3
=
Es R3
Is = I1 + I2 + I3
Is
I1
Es 120 Vdc
V1
V2
I2
V3 I3
Find the load current values and the total current supplied from the load.
R1 60
R2 30
R3 40
I1
=
Es R1
= 120 V 60
=
2A
I2
=
Es R2
= 120 V 30
=4A
I3
=
Es R3
=
120 V 40
=
3A
What is the value of Is?
Is = I1 + I2 + I3
Is = 2 A + 4 A + 3 A = 9 A
0.8 A
Is Es 120 V ac
0.8 A L1
0.8 A L2
Is = I1 + I2 + I3 Is = 0.8 A + 0.8 A + 0.8 A = 2.4 A
Find the equivalent resistance of the lamps shown. What is the value L3 of Is?
RL1
=
Es I1
= 120 V 0.8 A
= 150
RL1 = RL2 = RL3
R1
R2
RT RT is equivalent value of parallel resistors
RT draws the same current as R1 R2 and R3 in parallel.
Calculating Equivalent Parallel Resistances
R3
Two resistors only:
RT
=
R1R2 R1 + R2
Two or more resistors:
RT =
1
+
1
1 +1
+ ...
1
R1 R2 R3
RN
R1 50
R2 75
R3 80
Find RT for the circuit shown
Using two resistor formula twice
RT
=
R1R2 R1 + R2
RT1
=
50(75) 50 + 75
=
30
RT Using the other formula
RT =
1
+
1
1 +1
+ ...
1
R1 R2 R3
RN
RT
=
RT1R3 RT1 + R3
=
30(80) 30 + 80
=
21.82
RT =
1
+
1 1
+
1
50 75 80
RT
=
0.02 +
1 0.01333 +
0.0125
=
1 0.045833
=
21.82
ET 150
Coming Next: Electronic Component Data Sheets
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