The electrical circuits that are used in everyday electronics and appliances may seem confusing. But understanding the fundamental principles of electricity and magnetism that cause them to work can let you understand how different circuits differ from one another.

## Parallel vs. Series Circuits

To begin to explain the difference between series and parallel connections in circuits, you should first understand how parallel and series circuits differ from one another. **Parallel circuits** use branches that have different circuit elements, be them resistors, inductors, capacitors or other electrical elements, among them.

**Series circuits**, by contrast, arrange all of their elements in a single, closed loop. This means that **current**, the flow of charge in a circuit, and **voltage**, the electromotive force that causes current to flow, measurements between parallel and series circuits differ as well.

Parallel circuits are generally used in scenarios in which multiple devices depend upon a single power source. This ensures they can behave independently of one another so that, if one were to stop working, the others would continue working. Lights that use many bulbs can use each bulb in parallel with one another so each one can all light up independently of each other. Electrical outlets in households typically use a single circuit to handle different devices.

Though parallel and series circuits differ from one another, you can use the same principles of electricity to examine their current, voltage and **resistance**, a circuit element's ability to oppose the flow of charge.

For both parallel and series circuit examples, you can follow **Kirchhoff's two rules**. The first is that, in both a series and a parallel circuit, you can set the sum of the voltage drops across all elements in a closed loop equal to zero. The second rule is that you can also take any node or point in a circuit and set the sums of the current entering that point equal to the sum of the current leaving that point.

## Series and Parallel Circuit Methods

In series circuits, current is constant throughout the loop so that you can measure a single component's current in a series circuit to determine the current of all the circuit's elements. In parallel circuits, the voltage drops across each branch are constant.

In both cases, you use **Ohm's Law** *V = IR* for voltage *V* (in volts), current *I* (in amps or amperes) and resistance *R* (in ohms) for each component or for the entire circuit itself. If you knew, for example, the current in a series circuit, you could calculate the voltage by summing up the resistances and multiplying current by the total resistance.

**Summing up resistances** varies between parallel and series circuit examples. If you have a series circuit with different resistors, you can sum up the resistances by adding each resistor value to get the **total resistance**, given by the equation *R _{total} = R_{1} + R_{2} + R_{3}* ... for each resistor.

In parallel circuits, the resistance across each branch sums up to the **inverse of the total resistance** by adding their inverses. In other words, the resistance for a parallel circuit is given by *1/R _{total} = 1/R_{1} + 1/R_{2} + 1/R_{3} ...* for each resistor in parallel to represent the difference between series and parallel combination of resistors.

## Series and Parallel Circuit Explanation

These differences in summing resistance depend on the intrinsic properties of resistance. Resistance represents the circuit element's opposition to the flow of charge. If the charge were to flow in a closed loop of a series circuit, there is only one direction for current to flow, and this flow isn't split or summed up by changes in paths for the current to flow.

This means that, across each resistor, the flow of charge remains constant and the voltage, how much potential of charge is available at each point, differs because each resistor adds more and more resistance to this path of the current.

On the other hand, if the current from a voltage source such as a battery had multiple paths to take, it would split up as is the case in a parallel circuit. But, as stated previously, the amount of current entering a given point must equal how much current is leaving.

Following this rule, if current were to branch off into different paths from a fixed point, it should be equal to the current that re-enters into a single point at the end of each branch. If the resistances across each branch differ, then the opposition to each amount of current differs, and this would lead to differences in voltage drops across the parallel circuit branches.

Finally, some circuits have elements that are both in parallel and in series. When analyzing these **series-parallel hybrids**, you should treat the circuit as either in series or in parallel depending on how they're connected. This lets you re-draw the overall circuit using equivalent circuits, one of components in series and the other of those in parallel. Then use Kirchhoff's rules on both the series and the parallel circuit.

Using Kirchhoff's rules and the nature of electrical circuits, you can come up with a general method to approach all circuits regardless of whether they're in series or parallel. First, label each point in the circuit diagram with letters A, B, C, ... to make things easier for indicating each point.

Locate the junctions, where three or more wires connected, and label them using the currents flowing in and out of them. Determine the loops in the circuits and write equations describing how the voltages sum up to zero in each closed loop.

## AC Circuits

Parallel and series circuit examples differ in other electrical elements as well. In addition to current, voltage and resistance, there are capacitors, inductors and other elements that vary depending on whether they're in parallel or series. The differences between the types of circuit also depend on whether the voltage source uses direct current (DC) or alternating current (AC).

DC circuits let current flow in a single direction while AC circuits alternate current between forward and reverse directions at regular intervals and takes the form of a sine wave. The examples so far have been DC circuits, but this section focuses on AC ones.

In AC circuits, scientists and engineers refer to the changing resistance as **impedance**, and this can account for **capacitors**, circuit elements which store charge over time, and **inductors**, circuit elements which produce a magnetic field in response to the current in the circuit. In AC circuits, impedance fluctuates over time according to the AC power input while the total resistance is the total of the resistor elements, which remains constant over time. This makes resistance and impedance different quantities.

AC circuits also describe whether the direction of current is in phase between circuit elements. If two elements are **in-phase**, then the wave of the currents of the elements are in-sync with one another. These waveforms let you calculate **wavelength**, the distance of a full wave cycle, **frequency**, the number of waves which pass over a given point each second, and **amplitude**, the height of a wave, for AC circuits.

## Properties of AC Circuits

You measure the impedance of a series AC circuit using *Z = √R ^{2} + (X_{L} - X_{C})^{2}* for the

**capacitor impedance**

*X*and

_{C}**inductor impedance**

*X*

_{L}because the impedances, treated like resistances, are summed linearly as is the case with DC circuits.

The reason why you use the difference between the impedances of the inductor and capacitor instead of their sum is because these two circuit elements fluctuate in how much current and voltage they have over time due to the fluctuations of the AC voltage source.

These circuits are **RLC circuits** if they contain a resistor (R), inductor (L) and capacitor (C). Parallel RLC circuits sum up the resistances as *1/Z = √(1/R) ^{2} + (1/X_{L} - 1/X_{C})^{2}_the same way resistors in parallel are summed up using their inverses, and this value _1/Z* is also known as the

**admittance**of a circuit.

In both cases, you can measure the impedances as *X _{C }= 1/ωC* and

*X*for angular frequency "omega" ω, capacitance

_{L}= ωL*C*(in Farads) and inductance

*L*(in Henries).

Capacitance *C* can be related to voltage as *C = Q/V* or *V = Q/C* for charge on a capacitor *Q* (in Coulombs) and voltage of the capacitor *V* (in volts). Inductance relate to voltage as *V = LdI/dt* for change in current over time *dI/dt*, inductor voltage *V* and inductance *L*. Use these equations to solve for current, voltage and other properties of RLC circuits.

## Parallel and Series Circuit Examples

Though you can sum of the voltages around a closed loop as equal to zero in a parallel circuit, summing up the currents is more complicated. Instead of setting the sum of the current values themselves that enter a node equal to the sum of the current values leaving the node, you must use the squares of each current.

For an RLC circuit in parallel, the current across the capacitor and inductor as *I _{S }= I_{R} + (I_{L} - I_{C})^{2}* for supply current

*I*, resistor current

_{S}*I*, inductor current

_{R}*I*and capacitor current

_{L}*I*

_{C}using the same principles for summing the impedance values.

In RLC circuits, you can calculate the phase angle, how out-of-phase one circuit element is from the other, using the equation for phase angle "phi" *Φ* as *Φ = tan ^{-1}((X_{L} -X_{C})/R)* in which

*tan__*represents the inverse tangent function that takes a proportion as input and returns the corresponding angle.

^{-1 }()In series circuits, capacitors are summed up using their inverses as *1/C _{total} = 1/C_{1} + 1/C_{2} + 1/C_{3}*

_{}... while inductors are summed up linearly as

*L*... for each inductor. In parallel, the calculations are reversed. For a parallel circuit, capacitors are summed linearly

_{total }= L_{1}+ L_{2}+ L_{3}*C*..., and inductors are summed up using their inverses

_{total }= C_{1}+ C_{2 }+ C_{3}*1/L*... for each inductor.

_{total }= 1/L_{1}+ 1/L_{2}+ 1/L_{3}Capacitors work by measuring the difference in charge between two plates that are separated by a dielectric material between them which decreases voltage while increasing capacitance. Scientists and engineers also measure capacitance *C* as *C = ε _{0}ε_{r}A/d* with "epsilon naught" ε

_{0}as the value of the permittivity for air which is 8.84 x 10-12 F/m.

*ε*

_{r}_{}is the permittivity of the dielectric medium used between the two plates of the capacitor. The equation also depends on the area of the plates

*A*in m

^{2}and distance between the plates

*d*in m.