ROBO:Math

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Contents

Ohm's Law

The Biot-Savart Equation

Kirchoff's Laws

Kirchoff's Voltage Law (KVL)

Kirchoff's Current Law (KCL)

Resistance Calculations

Series Resistance

Resistors in series all share the same current. For two resistors to be in series a current must flow directly from the positive terminal of one resistor into the negative terminal of the other. The equivalent resistance is simply the sum of the resistances of the two resistors.

resistors in series.png

In general:

Series Resistance.gif

where N is the total number of resistors in series and R is each resistor's value in ohms. In other words, if you have three resistors (N = 3), of values 5, 8, and 3 ohms, the equivalent resistance of them connected in series would be 5 ohms + 8 ohms + 3 ohms = 16 ohms.

Parallel Resistance

Resistors in parallel are slightly more complicated (but not very much). Just like series resistors share a common current, parallel resistors share a common voltage. This is because their terminals are all connected to the source in essentially the same way. In stead of having the terminals of the resistors connected to one another, they all connect to one or the other terminals of the source. The equivalent resistance is the reciprocal of the reciprocal sum of the values of the resistors connected in parallel.

resistors in parallel.png

In general:

Parallel Resistance.gif

Just as before, N is the total number of resistors in the circuit and R is the resistor's values in ohms. But with them connected in parallel the same three resistors from the series example have to be added reciprocally so that you have:

Parallel Resistance step 1.gif

That is not, however your final value. Once you have the reciprocal sum, you need to take the reciprocal one more time:

Parallel Resistance step 2.gif

So the equivalent resistance for this parallel circuit is about 1.5 ohms.

Dividers

Combinations of resistors can be used to divide the voltage or current coming from a source. Circuits of this type are known as either Voltage Dividers or Current Dividers, depending on the configuration of the components.

Voltage Divider

The formula for a voltage divider is relatively simple. The output voltage is simply the ratio of the resistors to one another multiplied by the input voltage.

Voltage Divider Eqn.gif
Voltage Diider.png

In the circuit above, the 10 V source is VIN.gif, R1.gif is the 15k resistor, R2.gif is the 10k resistor and VOUT.gif is 4 V. So the voltage divider equation tells us: Voltage Divider Eqn Numbers.gif

Note that if we switch the position of the resistors we would get 6 V for the output instead of 4 V. An important application of this particular equation in Robotics is in the use of photoresistors.

Current Divider

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