There are three main elements to a basic circuit: (1) current, (2) voltage and (3) resistance. The flow of electrons in a circuit is called current (I) and current is given in units of amperes. The energy that drives the flow of electrons is called the voltage (V) and is given in units of volts. The voltage is measured between two points because it is the difference in energy (also known as the potential) that drives the current from one point to the next. The third term is resistance, which is measured in units of ohms (Ω). Resistance (R) is the opposition to the flow of current. One ohm is described as the level of resistance that will allow 1 ampere to flow when 1 volt is applied to a circuit.
Figure 1: A basic DC circuit, current flows from positive to negative.
Current is constantly run in a circuit to maintain power to loads, which are identified as resistors.
Recall that Ohm’s law describes the relationship between voltage, resistance and current. This is the basic equation used in circuit analysis.
Also review the real power equations, which are given in terms of watts.
Kirchhoff's LawsThere are two Kirchhoff laws that are necessary for the FE exam, (1) Voltage Law and (2) Current Law. The voltage law or KVL (Kirchhoff’s Voltage Law) states that the sum of voltages around a circuit loop is equal to zero. The current law or KCL (Kirchhoff’s Current Law) states that the sum of the current into and out of a node is equal to zero.
KVL describes the principle that in a circuit loop all voltage produced must be used by the devices in the circuit. There cannot be a change in voltage in a circuit loop.
Figure 2: The sum of the voltages around a loop must equal zero.
KVL is also applicable when there is more than one voltage source in a circuit, as seen in the next figure. Notice that the positive and negative terminals of the voltage sources are oriented in the same way, such that both voltage sources contribute positive voltage to the circuit.
Figure 3: The sum of the voltage around a loop with multiple voltage sources will equal zero.
If the terminals of the two voltage sources were instead situated opposite from one another, then one voltage source would contribute positive voltage and the other would contribute negative voltage. The voltage source that contributed negative voltage would be similar to charging a battery and the positive voltage contribution would be a discharging battery. KVL also applies to circuits with multiple loops. Each loop must he its voltage sum equal to zero.
Figure 4: KVL is applicable in any loop.
KCL describes the principle that the current entering any node in a circuit must equal the current leing the node. If you look at the previous circuit, specifically node “B”, you will notice that there is 240 A entering the node and 240 A leing the node, with 60 A leing on path B-C and 180 A leing on path B-E. The next equations show more examples of KCL for various nodes in the previous figure.
Circuit ArrangementsA complex circuit is made up of multiple devices and wires arranged in either series or parallel. These arrangements define the flow of current and the change in voltage with the following principles.
In a series circuit, the resistances are added to determine the equivalent resistance. Once you he a single equivalent resistance value, then you can determine the current flow through the circuit. The main concepts to understand are as follows: (1) Current is constant through a series circuit and (2) resistances are summed to determine equivalent resistance.
Figure 5: The equivalent resistance for resistors in series is found by adding the resistances.
Once the equivalent resistance is found, the current can be calculated: I=V/R_equiv=6A. Then, the voltage drop and power across each resistor can be found.
Figure 6: Voltage drop and power use in a series circuit.
Voltage Drop (Series): In the figure above, the voltage drop is found through each resistor by taking the current flow and multiplying it by the resistance, V=IR. As you can see, the voltage drops add up to 120V in accordance with KVL and the voltage drop magnitude varies directly with the resistance level in accordance with Ohm’s law.
In a parallel circuit, the voltage drop across each path is the same and the circuit splits between the different paths.
Figure 7: Equivalent resistance of resistances arranged in parallel.
The equivalent resistance will allow you to calculate the main circuit current as 87 amps. To calculate the current through each branch, notice that the voltages across each parallel resistor are the same.
Figure 8: Parallel circuits.
Voltage Drop: In the figure above, the voltage drop is found through each resistor by using KVL and realizing that in every loop the total voltage drop must equal to zero. Thus the voltage drop through resistors, (2 Ω), (8 Ω) and (10 Ω) are all equal to 120 V. The voltage drop through each resistor and the resistance value will allow you to determine the amount of current through each resistor.
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Multiple Sources (Superposition Theorem)A circuit with a single voltage or current source, such as those in the previous figures are easier to solve. However, when there are two voltage sources, each source will contribute current through a load.
In the simplest scenario of multiple sources, the following rules apply. If the voltage sources are in series, then they can easily be added to form an equivalent voltage source. If the current sources are in parallel, then can be added.
Figure 9: Voltage sources in series without anything between them can be added.
Figure 10: Current sources in parallel can be added to create an equivalent source.
When the circuit becomes more complex and there are multiple sources scattered throughout the circuit, the Superposition Theorem can be used. It basically says that for any linear circuit (i.e. circuits with only resistors, capacitors, and inductors) the current contributed from each separate source can be added together. To do this you must evaluate each source on its own, while turning off all other sources. When turning off sources, voltage sources become short circuits and current sources become open circuits.
This section is continued in more detail in the technical study guide . Also included are many more practice exam problems.