Electric circuits are basic parts of all electronic devices from radio and TV sets to computers and automobiles. Scientific measurements, from physics to biology and medicine, make use of electric circuits. We will apply the basic principles of electric current to analyze dc circuits involving combinations of batteries, resistors, and capacitors. We also study the operation of some useful instruments.
When we draw a diagram for a circuit, we represent batteries, capacitors, and resistors by the symbols. Wires whose resistance is negligible compared with other resistance in the circuit are drawn simply as straight lines.
Some circuit diagrams show a ground symbol which may mean a real connection to the ground, perhaps via a metal pipe, or it may simply mean a common connection.
This lesson focuses on Direct Current (DC), which is the foundation for understanding more complex circuits. It's crucial to distinguish it from Alternating Current (AC). While AC is used for power distribution, DC is fundamental to electronics, batteries, and many portable devices. The analysis techniques in this lesson apply specifically to DC circuits.
Direct Current (DC): The electric current flows in only one direction at a constant magnitude. The voltage provided by a DC source is steady. Some sources of the direct current may be Batteries, solar cells, or DC power supplies. The graph of DC current or voltage vs. time is a flat, horizontal line.
Alternating Current (AC): The electric current periodically reverses direction, oscillating back and forth, typically in a sinusoidal pattern. The voltage also alternates. Some sources of the alternating current may be Electrical grid (power outlets in homes), generators. The graph of AC current or voltage vs. time is a sine wave.
To have current in an electric circuit, we need a device such as a battery or an electric generator that transforms one type of energy into electric energy. Such a device is called a source of electromotive force or of emf. The potential difference between the terminals of such a source is called the emf of the source. The symbol $\xi$ is usually used for emf and its unit is volts.
A battery is not a source of constant current the current out of a battery varies according to the resistance in the circuit. A battery is, however, a nearly constant voltage source, but not perfectly constant as we now discuss. You may have noticed in your own experience that when a current is drawn from a battery, the potential difference (voltage) across its terminals drops below its rated emf.
The charge must move between the electrodes of the battery, and there is always some hindrance to completely free flow. Thus, a battery itself has some resistance, which is called its internal resistance; it is usually designated $r$.
A real battery is modeled as if it were a perfect emf in series with a resistor $r$. Since this resistance $r$ is inside the battery, we can never separate it from the battery. The two points a and b in the diagram represent the two terminals of the battery. What we measure is the terminal voltage:
$$ V_{ab}=V_a-V_b $$
When no current is drawn from the battery, the terminal voltage equals the emf, which is determined by the chemical reactions in the battery: However, when a current $I$ flows naturally from the battery there is an internal drop in voltage equal to $Ir$. Thus the terminal voltage (the actual voltage) is:
$$ V_{ab}=\xi-Ir $$
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A $65.0\Omega$ resistor is connected to the terminals of a battery whose emf is $12.0$V and whose internal resistance is $0.5\Omega$. Calculate the current in the circuit, the terminal voltage of the battery, $V_{ab}$, and the power dissipated in the resistor $R$ and in the battery’s internal resistance $r$.
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When two or more resistors are connected end to end along a single path, they are said to be connected in series.