Date post: | 22-Dec-2015 |
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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.
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.
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:
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:
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