Parallel Circuits - SIU

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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