Goal: To explore the usefulness of Resistors and to understand their applications to electronic circuits.

Objectives:1) What is a resistor and how is it useful?2) How resistances are found or made3) The different resistor combinations:

a) In seriesb) In Parallelc) Hybrid

4) Learn how to calculate how much the resistors affect the flow of current.

5) Power usage by resistors.

Why are resistors useful?

Resistors allow us to limit the flow of current in a

circuit.

How calculated?

• Larger conduits offer less resistance.• Some materials provide better flows than others.• The further something has to flow the more

resistance it will encounter.• So, R = ρ L / A• Here ρ is not density but is a substances

resistivity (which can be looked up for any substance).

• While there is a little dependence on temperature the resistivity mostly depends on the substance and only the substance.

• Examples will come in recitation.

Resistors in series:

Resistors in series:

Reff = R1 + R2 + R3 + R4

Sample:

• You have a circuit with 3 resisters:

• R1 = 4 Ohms

• R2 = 3 Ohms

• R3 = 9 Ohms

• What is the effective resistance of the circuit?

Sample:

• You have a circuit with 3 resisters:

• R1 = 4 Ohms

• R2 = 3 Ohms

• R3 = 9 Ohms

• What is the effective resistance of the circuit?

• R = R1 + R2 + R3 = 4 + 3 + 9 = 16 Ohms

Resistors in parallel:

Resistors in parallel:

1 1 1_

Reff = R1

+ R2If you remember to yesterday with that math trick this

would go to:R = R1 * R2 / (R1 + R2)

Resistors in parallel:

You have 2 resistors in parallel. R1 = 5 Ohms, R2 = 10 Ohms. What is the effective resistance?

Resistors in parallel:

So, R = 10 * 5 / (10 + 5)

R = 3.3 Ohms

Note that the resistance is lowered.

If just two resistors this simplifies to: R1 * R2

Reff =

R1 + R2

Hybrid resistor combinations:

Hybrid resistor combinations:

When faced with a hybrid of in series and in parallel, start by solving for the parallel portions, then solve for the in series portions.

Hybrid resistor combinations:

Reff = RAB + R3 + R45eff

R4 * R5 Reff = RAB + R3 +

R4 + R5

We will do an example in recitation.

Calculating the current:V = i R or i = V / R

So, in series:

i = V / Rtotal

In parallel:

For each branch, ibranch = V / Rbranch

And the total current is still i = V / Rtotal

Calculating the current for hybrids:For hybrid: i = V / Rtotal

For each branch of the

parallel portion, the

current is found by:

R45 i4 =

i *

R4 R4 * R5 R45 = R4 + R5

R5 _i4 =

i *

R4 + R5

Power

• Resisters use power.

• Power is an energy per time.

• This is measured in W

• Energy = Power * Time

• Energy is in Joules or Watt Hours

• Your electric company charges you on the energy you use (in kW-hrs).

Power for Resister

• For a Resistor the power it uses is just:

• P = IV = I2 R = V2 /R

• That’s all there is too it!

• For an entire circuit you use I, V, R for the entire circuit.

• For a single resistor or group of resistors, you use the I, V, R for those resistors.

Conclusion

• Resistors are very useful in controlling the amount of current present in a circuit.

• Resistors can be used in series or in parallel (to allow the same circuit to have different currents in different places).

• The total current in any circuit with just resitors is just:

i = V / Rtotal