DC Circuit

Meaning of DC Circuit

In a DC circuit, the current flows from the positive to the negative terminal of the battery. The constant direction of the current is displayed in Figure 1 below.

Fig. 1 - The flow of charge in a direct current circuit is always in the same direction.

This is a very basic depiction of what a DC circuit can look like. It consists of three key elements necessary for a circuit to function: an energy source (a battery), an energy consumer (a resistor), and conductive paths (wires).

In an ideal world, the energy source and the conductive paths would have negligible internal resistance. Such elements are known as ideal batteries and ideal wires. Even though these types of elements don't exist, we can make reasonable assumptions based on the circumstances.

If the circuit contains any other elements with resistance, we can ignore the internal resistance of the wires, as it's comparatively tiny. The internal resistance of an ideal battery can be determined by measuring the potential difference of the energy source across the terminals. This measurement is known as the electromotive force.

It's usually denoted by \(\varepsilon\) or "emf" and is measured in volts (\(\mathrm{V}\)).

Things get more complicated as we add more consumers to a DC circuit. In general, there are two ways of connecting elements in circuits: series and parallel. Let's look at each type more in-depth.

DC Series Circuit

The first way of assembling elements in a circuit is in series.

In a DC series circuit, the same current \(I\) is flowing through all components, without changing its direction.

Fig. 2 - A series circuit diagram consisting of three resistors.

A potential difference \(V\) occurs on each of the elements and differs depending on their resistance. The total potential difference can be expressed as

\[ V_\text{series}=\sum_{i=1}^n V_i=V_1+V_2+ \dots,\]

where \(n\) indicates the number of consumers.

All the resistors in the series connection can be replaced by one equivalent consumer, whose potential difference can be found by using the total resistance of all the resistors together rather than individually. The equation for finding the total resistance of a series connection is

\[R_\mathrm{series}=\sum_{i=1}^nR_i=R_1+R_2+ \dots.\]

As discussed earlier, in the case of a non-ideal battery, we also must account for its internal resistance. That can be done by simply treating the energy source as an additional resistor connected in series within the battery and the circuit. If there is a non-zero current flowing through the circuit, we can calculate the potential difference across the battery's terminals using the following equation:

\[\Delta V_\mathrm{terminal}=\varepsilon -Ir,\]

where \(\Delta V_\mathrm{terminal}\) is the potential difference between the battery’s terminals, \(\varepsilon\) is the electromotive force, \(I\) is the current, and \(r\) is the internal resistance of the battery.

DC Parallel Circuit

The other circuit type to consider is parallel.

The electric current \(I\), flowing from the positive pole of the source, is divided among all elements and then merges again at the negative pole of the battery. Even with all the additional paths, the direction of the flow of charges remains constant.

Fig. 3 - A parallel circuit diagram consisting of three resistors.

In a parallel circuit, the potential difference \(V\) is the same across each path, provided by the electromotive force of the power source. The total current, on the other hand, is the sum of the current through the individual components:

\[ I_\text{parallel}=\sum_{i=1}^n I_i=I_1+I_2+\dots,\]

where \(n\) once again indicates the number of consumers.

Finally, the reciprocal of the total resistance is the sum of the reciprocals of all consumer resistances:

\[\frac{1}{R_\mathrm{parallel}}=\sum_{i=1}^n\frac{1}{R_i} =\frac{1}{R_1}+\frac{1}{R_2}+\dots.\]

DC Circuit Rules

All the circuit rules relevant to this topic are compiled in the table below.

Table 1 - DC circuit rules.

AC vs. DC Circuits

Another way in which current can flow is known as alternating current.

In the AC circuit displayed below, instead of a battery, there is an AC power supply. It creates alternating waves of current which move back and forth, rather than having a constant direction like in the DC circuit case.

Fig. 4 - Alternating current periodically changes its direction.

Considering it's a periodic event, alternating current can be described using frequency, measured in hertz (\(\mathrm{Hz}\)). It quantifies the number of times the flow of charges changes direction per second.

AC circuits are commonly used in producing and transporting electricity, as well as powering electric motors. The electric grid provides us with alternating current, which is then converted into direct current through adapters, when charging batteries, for instance.