Circuits

Electricity is useful in its own right but if we want to be able to apply it to appliances, electronic devices, and more in the real world, it has to be ordered in a way that is useful to us. Circuits allow us to utilize electronic devices properly by putting them through loop-like paths where moving electric charges, called current, flow. In these paths, the charges encounter devices that can take away electric potential from the charges. These devices are usually electronic appliances like lightbulbs, for example. A more general term for them in DC Circuits is resistors.

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RC Circuits are circuits that still run on direct current, except they have a capacitor somewhere in the circuit.

Below are the topics for circuits:

Current

Resistance

Ohm's Law

Electric Power

DC Circuits

RC Circuits

Charging

In circuit analysis, we use schematics, which can also be called circuit diagrams, to visualize the different devices at play acting on currents in the circuit.

The circuit above is an extremely simplistic circuit schematic that showcases an emf source at the bottom, which supplies electrical voltage to the circuit and allows charges to flow around the circuit in loops. The device at the top is a resistor that provides resistance to the charges and slows them down. DC Circuits in physics problems always take on the direction of conventional current, the direction in which positive charges would move in. Thus, they go out from the positive terminal of a battery and in through the negative terminal. However, in real life, electrons(negative charges) are the particles in flow so real circuits flow opposite to conventional circuits.

Provided below is a reference to a handful of different US-based circuit analysis symbols:

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Battery(EMF Source)

Wire

Wire

Wire

Ammeter

Voltmeter

DC Source

Earth(Grounding)

Series circuits are circuits where all the resistors are lined up in a chain, singular path for current to flow through. A series circuit looks like the one below:

In this diagram, all the resistors are lined up in a chain-like format. The same charges, flowing as current, flow through all of these resistors.

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Series circuits have some very useful characteristics which make circuit analysis on them much easier.

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1)The current through a series circuit is conserved because there is only one path for it to flow through. This also means all the resistors in a series circuit receive the total current(the emf divided by total resistance)

2)The sum of the voltage drops across the individual resistors in a series circuit equals the total voltage drop through the series circuit.

3)The sum of the individual resistances of the resistors in a series circuit equals the total resistance of the series circuit.

In an RC(Resistor-Capacitor) Circuit, the total capacitance of the capacitors in a series circuit is equal to the reciprocal of the sum of the reciprocals of their individual capacitances.

If you disconnect the circuit in a series circuit at any point, then the entire circuit breaks down and stops working.

A circuit has parallel components if there are more than 1 path for current to flow through. A circuit diagram for a parallel circuit looks like this.

In the bottom portion of the circuit, the circuit breaks up into two paths for current to flow through. If we take the two nodes(endpoints) of the parallel component, the change in electric potential will be the same in both portions.

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Therefore, the first and foremost rule for parallel circuits is that

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1)The voltage across all the paths and their elements in a parallel circuit is constant.

2)The current through the individual components of the parallel component of the circuit sum to the total current through the circuit prior to reaching the node.

3)The reciprocal of the total resistance of all the resistors in a parallel component of a circuit is the sum of the reciprocal of the total resistance of the individual paths in the parallel component.

1)Kirchhoff's Current Law(also called the Junction Rule) basically states that the total current entering a node equals the total current exiting the node.

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This law is derived simply from the conservation of electric charge. The amount of charge flowing through the circuit doesn't change so if the current splits up into multiple paths, the combined currents from the two paths equal the total current before the charges separated.

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2)Kirchhoff's Voltage Law(also called the Loop Rule) states that the change in total voltage across a loop is 0. This law's premises are purely founded on the conservation of energy. No charges went anywhere outside the circuit so their electric potentials are still intact.

This law is derived simply from the conservation of electric charge. The amount of charge flowing through the circuit doesn't change so if the current splits up into multiple paths, the combined currents from the two paths equal the total current before the charges separated.

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2)Kirchhoff's Voltage Law(also called the Loop Rule) states that the change in total voltage across a loop is 0. This law's premises are purely founded on the conservation of energy. No charges went anywhere outside the circuit so their electric potentials are still intact.

This rule can be evaluated with the circuit below.

As you can see, the voltage taken up out of every individual component of the circuit sums up to the total voltage supplied into the circuit through the battery. This is the guiding principle behind Kirchhoff's Voltage Law.

RC Circuits are direct-current(DC) Circuits that compose not only resistors but both resistors and capacitors alike.

Conceptually, RC Circuits heavily deal with the flows of charges to the capacitor as time elapses. Once the voltage source turns on, charges build up on both plates of the capacitor. However, as more charges build up on the plates, there will stronger repulsion of charges due to more like charges being on the capacitor plates. This stronger repulsion will result in a reduction of current through the capacitor and so as time goes on, the current will decrease from its initial value, given by

and asymptotically approach a value of 0 A as the time tends to infinity. Since the capacitor is initially discharged, it has an initial voltage of 0 V. However, as charges buildup, the voltage tends to the emf supplied by the emf source because

and Q increases as time elapses.

Ammeters are measuring devices that measure current in DC circuits. Ammeters are directly inserted into the circuit in series with other components.

Ammeters actually hold resistances of their own; in fact, they have to in order to measure current properly. However, this resistance is almost negligible so it's enough to measure an accurate current but not enough to the dynamics of the circuit itself.

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Voltmeters are measuring devices that measure the voltage across any two given points in a DC Circuit. Voltmeters are connected in parallel with other components in the circuit. Standard voltmeters have two ends

Like ammeters, voltmeters have internal resistances of their own but they don't alter the circuit because they're so large. Because the voltmeter resistance is so large, negligible current flows to it and so voltage measurements given by them are still accurate.