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Definition of Direct Current
To understand the concept of a direct current circuit, we first must understand what exactly is direct current.
In a closed electric circuit, current \(I\) flows only if there is a potential difference \(V\) between the poles of the power source. This potential difference can be achieved and maintained by doing work done by external forces.
One way of achieving that is by converting chemical energy into electrical energy through chemical reactions. These occur in electrolytes, which are chemicals that conduct electricity due to the presence of positively and negatively charged ions. When electrodes of two different metals are immersed in an electrolyte, ions transfer electric charges between the electrodes, creating a potential difference between them. In this case, the work done happens at the expense of the chemical energy of the system.
That's how all voltaic cells and batteries operate, resulting in something known as a DC voltage which induces a direct current.
Direct current (DC) is the flow of electric charge in one direction.
Now let's apply this concept to a simple 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.
This is the conventional flow of current. In actuality, negatively charged electrons are attracted to the positively charged end of the battery, so electrons travel opposite to the defined current flow.
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.
Electromotive force is the amount of energy a battery supplies per unit charge that passes through it.
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.
A series connection is one in which circuit elements are connected such that any charge passing through one element must proceed through the other and has no other path available between them.
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.
A parallel connection is one in which charges may pass through one of two or more paths.
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.
| Name | Equation | Variables |
| Ohm's law | \(I=\frac{\Delta V}{R}\) | \(I\) - current\(V\) - electric potential\(R\) - resistance |
| Power in an electric circuit | \(P=I\Delta V= I^2R=\frac{\Delta V^2}{R}\) | \(P\) - power\(I\) - current\(V\) - electric potential\(R\) - resistance |
| Resistance in a parallel circuit | \(\frac{1}{R_\mathrm{parallel}}= \sum_{i=1}^n\frac{1}{R_i}\) | \(R\) - resistance |
| Resistance in a series circuit | \(R_\mathrm{series}=\sum_{i=1}^nR_i\) | \(R\) - resistance |
| Potential difference between battery's terminals | \(\Delta V_\mathrm{terminal}=\varepsilon -Ir\) | \(I\) - current\(V\) - electric potential\(\varepsilon\) - emf\(r\) - internal resistance |
| Energy changes in an electric circuit | \(\Delta U_\mathrm{elec}=q\Delta V\) | \(U\) - potential energy\(q\) - point charge\(V\) - electric potential |
| Kirchhoff's loop rule | \(\sum \Delta V = 0\) | \(V\) - electric potential |
| Kirchhoff's junction rule | \(\sum I_\mathrm{in}=\sum I_\mathrm{out}\) | \(I\) - current |
AC vs. DC Circuits
Another way in which current can flow is known as alternating current.
Alternating current (AC) is the flow of electric charge that periodically changes directions.
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.
DC Circuit - Key takeaways
- Direct current (DC) is the flow of electric charge in one direction.
- Ideal batteries and ideal wires have negligible internal resistance.
- Wires can be assumed to be ideal if other elements in the circuit have resistance.
- Electromotive force is the amount of energy a battery supplies to every charge that passes through it.
- A series connection is one in which circuit elements are connected such that any charge passing through one element must proceed through the other and has no other path available between them.
- A non-ideal battery can be treated as a resistor connected in series within the circuit.
- A parallel connection is one in which charges may pass through one of two or more paths.
- Alternating current (AC) is the flow of electric charge that periodically change directions.
References
- Fig. 1 - DC circuit diagram, StudySmarter Originals.
- Fig. 2 - A series circuit diagram, StudySmarter Originals.
- Fig. 3 - A parallel circuit diagram, StudySmarter Originals.
- Fig. 4 - AC circuit diagram, StudySmarter Originals.
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Frequently Asked Questions about DC Circuit
What is a DC circuit?
A DC circuit is a circuit in which the flow of electric charge goes in one direction.
How does an inductor work in a DC circuit?
An inductor is an element that allows direct current and stops alternating current from flowing through it.
What causes voltage drop in a DC circuit?
A voltage drop in a DC circuit is caused by current passing through the circuit.
What does a diode do in a DC circuit?
In a DC circuit, a diode acts as a switch for the current by allowing the flow in one direction and restricting it in the opposite.
How capacitor works in DC circuit?
In a DC circuit, a capacitor blocks the direct current.
How does current flow in a DC circuit?
In a DC circuit, current flows in one direction.
How to amplify current in DC circuit?
In a DC circuit, the current can be amplified by using a transistor.
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