The current is found using Ohm’s law,
. Entering the value of the applied voltage and the total resistance yields the current for the circuit:
Strategy and Solution for (c)
The voltage—or
drop—in a resistor is given by Ohm’s law. Entering the current and the value of the first resistance yields
Similarly,
and
Discussion for (c)
The three
drops add to
, as predicted:
Strategy and Solution for (d)
The easiest way to calculate power in watts (W) dissipated by a resistor in a DC circuit is to use
Joule’s law ,
, where
is electric power. In this case, each resistor has the same full current flowing through it. By substituting Ohm’s law
into Joule’s law, we get the power dissipated by the first resistor as
Similarly,
and
Discussion for (d)
Power can also be calculated using either
or
, where
is the voltage drop across the resistor (not the full voltage of the source). The same values will be obtained.
Strategy and Solution for (e)
The easiest way to calculate power output of the source is to use
, where
is the source voltage. This gives
Discussion for (e)
Note, coincidentally, that the total power dissipated by the resistors is also 7.20 W, the same as the power put out by the source. That is,
Power is energy per unit time (watts), and so conservation of energy requires the power output of the source to be equal to the total power dissipated by the resistors.
Major features of resistors in series
Series resistances add:
The same current flows through each resistor in series.
Individual resistors in series do not get the total source voltage, but divide it.
Resistors in parallel
[link] shows resistors in
parallel , wired to a voltage source. Resistors are in parallel when each resistor is connected directly to the voltage source by connecting wires having negligible resistance. Each resistor thus has the full voltage of the source applied to it.
Each resistor draws the same current it would if it alone were connected to the voltage source (provided the voltage source is not overloaded). For example, an automobile’s headlights, radio, and so on, are wired in parallel, so that they utilize the full voltage of the source and can operate completely independently. The same is true in your house, or any building. (See
[link] (b).)
To find an expression for the equivalent parallel resistance
, let us consider the currents that flow and how they are related to resistance. Since each resistor in the circuit has the full voltage, the currents flowing through the individual resistors are
,
, and
. Conservation of charge implies that the total current
produced by the source is the sum of these currents:
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