Measure resistance by comparison
================================

According to Ohm's law, current through a conductor and the potential difference between it's end are proportional. The constant of proportionality is called the resistance. Mathematically :math:`R =\frac{V}{I}`. When two resistors are connected in series, the current will be same through both. :math:`I=\frac{V_{1}}{R_{1}}=\frac{V_{2}}{R_{2}}`. if the value of one resistance and the voltage across both are known, the other resistance can be calculated from  
:math:`R_{1}=R_{2}\times\frac{V_{1}}{V_{2}}`

Objective
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Find the value of an unknown resistance by comparing it with a known resistance, using the equations given above.
Assume R1 is the unknown resistance and R2 is :math:`1000\Omega`

.. image:: schematics/res-compare.svg
	   :width: 300px

Procedure
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-  Fix the two resisters in series on a bread board.
-  Connect the junction to A1
-  Connect the other end of R2(:math:`1~k\Omega`) to Ground.
-  Connect one end of R1 to PV1
-  Set PV1 to 4 volts.
-  Enable the Checkbutton on top right, to measure the DC voltage at A1.

Current :math:`I = \frac{V_{A1}}{R_{2}}` and R1 can be calculated using
:math:`R_{1} = \frac {V_{PV1} - V_{A1}}{I}`.

Ohm's law in AC circuits
------------------------
It can be easily shown that this measurement can be done using AC also. We will use both A1 and A2 inputs here.

-  Fix the two resisters in series on a bread board.
-  Connect the junction to A2
-  Connect the other end of R2(:math:`1~k\Omega`) to Ground.
-  Connect one end of R1 to both WG and A1
-  Set WG to 1000Hz
-  Enable A1 and A2
-  Enable the Cursor Check button to diplay the voltages at the cursor

Taking voltage reading from the picture below, one can calculate the value of one resistor if the other is known. 

.. image:: pics/res-compare-ac.png
	   :width: 400px
 
Discussion
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In this measurements we have made the assumption that no current flows in to A1 and A2. This is not true, they both have an input impedance of :math:`1M\Omega` . This will matter when we use resistance values of mega Ohms range. To illustrate this
connect WG to A1 using a wire and the same signal to A2 through a :math:`1M\Omega`  resistor. Try to explain the results using Ohm's law.

