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Author Topic: Math: Ohm's Law w/Amplifiers  (Read 824 times)
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I have a couple mathematical questions about Ohm's law and amplifiers.

First question (no amplifier): If I have a 9V battery, how can I calculate the battery's mA and Ω output?

Second question: If I have an Arduino pin hooked up to the base of an P2N2222A how can I calculate the V, mA, and Ω output of the collector of the P2N2222A?
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First question (no amplifier): If I have a 9V battery, how can I calculate the battery's mA and Ω output?

It's not clear what you are asking for.  The current drawn from the battery (mA) will depend on the resistance of the load (Ω).  The current in Amps is equal to the Voltage divided by the resistance in Ohms.  If you have a 9V battery it will push 9 mA through a 1000Ω load.  The faster you draw current out of a battery the shorter its life will be.



Second question: If I have an Arduino pin hooked up to the base of an P2N2222A how can I calculate the V, mA, and Ω output of the collector of the P2N2222A?

Transistors have a characteristic called 'beta' which is the current gain.  for the P2N2222A the beta is about 100.  If you are using an Arduino pin to drive it you are limited to an absolute maximum of 40 mA from the pin (30 mA would be better) so the switchable current should be 3 A, but that is probably more than the transistor can stand.  Depending on the transistor the maximum will be between 500 mA and 1 A.
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Second question: If I have an Arduino pin hooked up to the base of an P2N2222A how can I calculate the V, mA, and Ω output of the collector of the P2N2222A?

Well technically a transistor doesn't output a voltage or current on it's collector. It however assumes a emitter/collector resistance that allows the external collector's load and load source voltage to determine maintain a specific current flow depending on it's base current times it beta gain. One should be careful and not try and over simplify the operation of a transistor as much is dependent on the external circuit that the transistor is wired in.

Lefty

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fuzzball27,

Are you intending to ask what the "Output Impedance" of the battery & transistor is?

See the last paragraph here:

http://en.wikipedia.org/wiki/Current_source
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I have a couple mathematical questions about Ohm's law and amplifiers.

First question (no amplifier): If I have a 9V battery, how can I calculate the battery's mA and Ω output?

Second question: If I have an Arduino pin hooked up to the base of an P2N2222A how can I calculate the V, mA, and Ω output of the collector of the P2N2222A?

You can't calculate the battery's specifications, you can look them up in a datasheet or measure them.  And batteries usually have a voltage, internal resistance, max discharge rate and capacity - not sure what you mean by "mA and Ω output"

For a transistor circuit you need some more information - which circuit configuration (common base, common emitter or emitter-follower), the various biasing resistors and supply voltage and the typical gain of the transistor.  Negative feedback also affects the effective impedance at the output of an amplifier too.

I'm not sure if you are asking for a set of equations for the various circuit configurations or have in mind a particular circuit...
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For question one, this is what I was looking for:
Quote
If you have a 9V battery it will push 9 mA through a 1000Ω load.

As for the second question, let me rephrase it into an example for clarity. I want to connect a PWM output (from the Arduino) to the base of my P2N2222a, connect the emitter of the transistor to ground, and connect the collector to the load. How can I determine mA, Ω, and V between the collector and the load? (In a mathematical equation please)

A side question: How can I connect an external power supply into my example circuit?
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For question one, this is what I was looking for:
Quote
If you have a 9V battery it will push 9 mA through a 1000Ω load.

As for the second question, let me rephrase it into an example for clarity. I want to connect a PWM output (from the Arduino) to the base of my P2N2222a, connect the emitter of the transistor to ground, and connect the collector to the load. How can I determine mA, Ω, and V between the collector and the load? (In a mathematical equation please)


What is missing in your 'example for clarity' is

1. Resistor size between pwm output pin and base of transistor. Without a resistor the output pin will burn out. The size of the resistor is one variable that contributes to how much current the transistor can pass from collector to emitter.

2. Load resistance. This is a variable that will also effect how much collector/emitter current flows.

3. Load voltage. This is a variable the will also effect collector/emitter current flow amount.

Quote
A side question: How can I connect an external power supply into my example circuit?


If you mean just to power an external load device wired to a switching transistor under control of a arduino output pin, then:

Positive of supply wires to one side of the load device. Negative side of supply wires to emitter of transistor AND to arduino ground pin.


Lefty

« Last Edit: September 15, 2011, 05:26:42 pm by retrolefty » Logged

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1. Resistor size between pwm output pin and base of transistor.

smiley-razz    2.2kΩ

Quote
2. Load resistance.

I'm not sure, (I've been searching for a while now.)

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3. Load voltage.

9V DC

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Positive of supply wires to one side of the load device. Negative side of supply wires to emitter of transistor AND to arduino ground pin.

Do you mean that I need to put both the Arduino and the external power supply ground/power into the same places on the circuit? (respectively)
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Quote

Quote
1. Resistor size between pwm output pin and base of transistor.

    2.2kΩ


This resistor is call R b . YOU have to have this resistor between Arduino pin and a base of a transistor ( NPN or PNP )
The value I use are : 1K, 2.2 K , 3.3 K, 4.7 K  are OK. The goal is to not overload the Arduino pin.

Quote

Quote
2. Load resistance.

I'm not sure, (I've been searching for a while now.)


When design a transistor switching circuit, You need : Supply voltage, load resistance and you simply calculate the current.

Like : I = V / R  Example :  9 V / 1 K = 9 mA    With that information ( 9 mA and 9 V ) , you can select the type of transistor to use by looking at the datasheet of transistor for Ic ( max ) ,  Vcb (max ) , Power value ( max ) .   In this example, a transistor like 2N3904 is OK.

Quote

Quote
Positive of supply wires to one side of the load device. Negative side of supply wires to emitter of transistor AND to arduino ground pin.

Do you mean that I need to put both the Arduino and the external power supply ground/power into the same places on the circuit? (respectively)


Arduino power and power for the circuit is seperated. But the gnd goes together. Example : 5 V for the Arduino, 9 v for the transistor circuit is seperated  and gnd of Arduino AND gnd of the transistor circuit connect together.

I hope you understand.
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I understand. Thank you all very much, I've gotten everything working properly.
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