Correct use of Ohm's Law
One of the most common mistakes made by beginning electronics
students in their application of Ohm's Laws is mixing the contexts
of voltage, current, and resistance. In other words, a student might
mistakenly use a value for I through one resistor and the value for
E across a set of interconnected resistors, thinking that they'll
arrive at the resistance of that one resistor. Not so! Remember this
important rule: The variables used in Ohm's Law equations must be
common to the same two points in the circuit under
consideration. I cannot overemphasize this rule. This is especially
important in series-parallel combination circuits where nearby
components may have different values for both voltage drop and
current.
When using Ohm's Law to calculate a variable pertaining to a
single component, be sure the voltage you're referencing is solely
across that single component and the current you're referencing is
solely through that single component and the resistance you're
referencing is solely for that single component. Likewise, when
calculating a variable pertaining to a set of components in a
circuit, be sure that the voltage, current, and resistance values
are specific to that complete set of components only! A good way to
remember this is to pay close attention to the two points
terminating the component or set of components being analyzed,
making sure that the voltage in question is across those two points,
that the current in question is the electron flow from one of those
points all the way to the other point, that the resistance in
question is the equivalent of a single resistor between those two
points, and that the power in question is the total power dissipated
by all components between those two points.
The "table" method presented for both series and parallel
circuits in this chapter is a good way to keep the context of Ohm's
Law correct for any kind of circuit configuration. In a table like
the one shown below, you are only allowed to apply an Ohm's Law
equation for the values of a single vertical column at a
time:
Deriving values horizontally across columns is allowable
as per the principles of series and parallel circuits:
Not only does the "table" method simplify the management of all
relevant quantities, it also facilitates cross-checking of answers
by making it easy to solve for the original unknown variables
through other methods, or by working backwards to solve for the
initially given values from your solutions. For example, if you have
just solved for all unknown voltages, currents, and resistances in a
circuit, you can check your work by adding a row at the bottom for
power calculations on each resistor, seeing whether or not all the
individual power values add up to the total power. If not, then you
must have made a mistake somewhere! While this technique of
"cross-checking" your work is nothing new, using the table to
arrange all the data for the cross-check(s) results in a minimum of
confusion.
- REVIEW:
- Apply Ohm's Law to vertical columns in the table.
- Apply rules of series/parallel to horizontal rows in the
table.
- Check your calculations by working "backwards" to try to
arrive at originally given values (from your first calculated
answers), or by solving for a quantity using more than one method
(from different given values).
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