Download 4.1 Ohm`s Law of Resistance to Current Electric current is the motion

4.1 Ohm's Law of Resistance to Current
Electric current is the motion of electric charges due to presence of the external
electric field. The absolute value of electric current is defined as the charge carried
through the cross section of the conductor per unit of time:
I
dq
dt
When current moves through a wire due to an electrical potential difference (a voltage), it
is literally electric charges falling through the wire due to an electrical field. This is
completely analogous to gravitational charges (masses) falling through the air due to a
gravitational field. Different types and sizes (gauges) of wire resist this current by
different amounts. Ohm's Law describes (for some materials) just how this resistance
affects a current for a specified voltage, i.e., it relates the current to the voltage. The goal
of this experiment is to be able to “discover” Ohm's law. Furthermore, we will investigate
the effect of multiple resistors on current.
Think about possible types of relationships between voltage and electric current.
What kind of relation you would expect in a simple case of the regular metal wire?
Lab Experiment
In the diagrams, A is an ammeter, which measures the current in amps (A),
milliamps (mA), or microamps (μA). These measure the current through a resistor and
must be placed in series with the resistor. Two circuit elements are “in series” if all of the
current which goes through one also goes through the other. Current is the flow of charge
(an amount of material); it does not diminish as it passes through the circuit elements.
Also, V is a voltmeter, which measures the voltage in volts (V). These measure the
voltage across (the potential difference from before to after) a resistor and must be placed
in parallel with the resistor. Two circuit elements are “in parallel" if the current gets split
between one and the other. Voltage is related to the energy of the charges; it does
diminish (or increase) as it passes through the circuit elements.
Build the circuit in Figure below using your first resistor. Measure the current (from
the ammeter) for several voltage values (as measured from voltmeter). Figure out Ohm's
Law by graphing the voltage, V, versus the current, I, and considering the equation of the
best trendline. The coefficient of the linear term is the resistance of the resistor, R. How
does this compare (%-difference) to the labeled value? (Consult your instructor on how to
read resistor’s color code) Repeat this for the second resistor.
Notice that you have a choice of where to put the voltmeter. On the left, the
voltmeter is not truly in parallel with the resistor. On the right, the ammeter is not truly in
series with the resistor. You will be making a mistake either way, but hopefully neither is
too wrong. For one resistor only, measure this both ways and see how large the effect is.
The small circles are the connections for the wires.
Build the circuit in the left side of the next figure using your two resistors. Measure
current, I, from ammeter A for several voltages, V. Graph the voltages V1 ,V2 and Vt on
the same graph, all versus the current I. Consider the equation of the best trendline. Use
your determined form of Ohm's Law to decide on the single equivalent resistor which
could replace your two resistors without changing the current-voltage relationship. Is the
equivalent resistor larger than or smaller than the individual resistances? Determine a
relationship between your resistors R1 , R2 , and the equivalent resistance Req .
Build the circuit in right side of the next figure using your two resistors. Measure
current, I, from each ammeter A ( I1 , I 2 , and I t ) for several voltages V. All on the same
graph, plot the voltage V versus each current. Consider the equation of the best trendline.
Use your determined form of Ohm's Law to decide on the single equivalent resistor
which could replace your two resistors without changing the current-voltage relationship.
Is the equivalent resistor larger than or smaller than the individual resistances?
Determine a relationship between your resistors R1 , R2 , and the equivalent resistance Req .
(Hint: It may help to consider reciprocals of certain values.)