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Circuit Examples

Identify and describe series and parallel circuits.

Simplify those circuits.

Calculate the current and/or voltage of each part of a circuit.

By observing and participating in this lesson, you will be able to:

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Series and Parallel Circuits

Electrical components can be connected in various ways. This drastically changes the properties of the circuit.

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Series Circuits

One simple way to arrange components in an electrical circuit is to create one large continuous loop with the components:

2 batteries

switch

Light bulb

resistor

This is similar to a TV series where one episode follows another.

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Parallel Circuits

Another way to connect a circuit is in parallel. In this arrangement, each component is connected separately in its own “loop”.

2 batteries

3 resistors in parallel

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Resistors in Parallel

To find the equivalent resistance of resistors added in parallel:

...R

1

R

1

R

1

R

1

321P

Parallel or total combined

resistance, ΩIndividual

resistors, Ω

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Parallel Resistor Example

Calculate the total effective resistance of two 10 Ohm resistors connected in parallel.

21P R

1

R

1

R

1

10Ω

1

10Ω

1

R

1

P

10Ω

2

R

1

P

5ΩRP

Take the reciprocal of each side of

equation

Combine, use common

denominator if needed

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Parallel Resistor Observations

5 Ohms. Notice that the total overall resistance is lower than either one of them individually!

This occurs because there are multiple paths for the electrons to take, lowering their resistance.

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Circuit Problems

This section will detail how to calculate the various electrical quantities in a circuit.

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Series Circuit

Calculate the current and electric potential difference for each component of the circuit shown.

R2=

10Ω

R1=5Ω

5V

A good first step is to simplify the circuit.

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Circuit Simplification

R2=

10Ω

R1=5Ω

5V

Because this is a series circuit, to combine the resistors and simplify the circuit, they are merely added together.

5V

Rs=

15Ω

...RRRR 321S

15Ω10Ω5ΩRS

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Current in a Series Circuit

5V

Rs=

15Ω

Use the voltage of the power supply and the total resistance of the circuit to find the total current flowing through the circuit.

Because the electron flow has no where else to go, this amount is also the current flowing through both resistors. I1 and I2 is that same .33 Amperes.

IRV

R

VI

.33A15Ω

5VI

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Voltage in a Series Circuit

R2=

10Ω

R1=5Ω

5V

Since we know the current flowing through each resistor, we can use Ohm’s law to find the potential difference for each of those resistors.

IRV1

) (.33A)(5ΩV1

1.67VV1 Notice how the sum of the two voltages adds up to the power supply for the circuit.

IRV2

) (.33A)(10ΩV23.33VV2

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Parallel Circuit

Calculate the current and electric potential difference for each component of the circuit shown.

5V

R1=5Ω R2=10Ω

Notice how this parallel circuit contains the exact same components as the series circuit, they are just arranged differently.

Again, a good first step is to simplify the circuit.

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Circuit Simplification

21P R

1

R

1

R

1

5V

R1=5Ω R2=10Ω

10Ω

1

5Ω

1

R

1

P

10Ω

1

10Ω

2

R

1

P

10Ω

3

R

1

P

3.3ΩΩ3

10RP

Notice this parallel resistance is less than either one individually.

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Shortcut Formula

An equivalent formula can be used for two resistors, R1 and R2, connected in parallel. Sometimes this formula is easier to manipulate.

21

21P RR

RRR

It may be easier to remember this formula as the product over the sum for the two resistors.

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Voltage in a Parallel Circuit

5V

R1=5Ω R2=10Ω

The easy part about any parallel circuit is the voltage applied to each item.

Since each item has its own independent connection to the battery or power supply, each item receives that potential.

In this case, V1 and V2 are each 5V.

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Current in a Parallel Circuit

5V

R1=5Ω R2=10Ω

Once you realize that the electric potential for each resistor is 5V, finding the current is easy using Ohm’s law, V=IR.

1

11 R

VI

2

22 R

VI

1A5Ω

5VI1 .5A

10Ω

5VI2

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Current Observations

5V

R1=5Ω R2=10Ω

Notice the two currents add up to the same value as the total current in the circuit. This is a good way to check your work.

1.5A3.3Ω

5V

R

VI

TT

1.5A.5A1AIII 21T

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Conclusion

You should now be able to describe series and parallel circuits with words and numbers!

Questions???

Homework:

Check with your instructor