One the the significant roles that electrical engineering dram in our society is permitting the infection of power from once location to another, even if it is it is to strength a bionic contact lens or a data center. Over there are countless units that energy depending upon the context, such together calories because that food or tons of TNT for explosives, yet in electrical engineering we generally measure energy in the SI obtained unit dubbed joules, v symbol J. To express in SI base units, \$1 ext J = 1 ext kgcdot extm^2 / exts^2\$.The law of conservation of energy asserts the the complete of power of a closed mechanism is constant; in other words, energy can no be developed nor destroyed, just converted native one type into another. Let us research this principle once a battery is connected to a light bulb.

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Figure 1 Fig. 1: Let over there be light! The battery, presented with confident \$(+)\$ terminal in ~ the optimal and an adverse \$(-)\$ terminal in ~ the bottom, offers the energy that provides the light pear shine.
Inside a battery, a chemistry (redox) reaction drives hopeful ions in the direction of the battery"s confident terminal and an adverse ions towards its an adverse terminal. When the battery"s terminals are associated through the light bulb, a pathway is created for charge to flow. Negatively fee electrons circulation from the \$-\$ terminal come the \$+\$ terminal with the irradiate bulb. This flow of fee converts chemistry potential power into electrical energy.In the light bulb, the circulation of charge through the filament heats it up and causes it come glow. In this way, the light bulb converts electrical energy to heat energy and also light energy.

Figure 2 Fig. 2: conservation of energy. In the device in Fig. 1, chemistry potential energy is converted to electric energy, i m sorry is instantly converted to light energy and heat energy. Through the conservation of energy, the joules of chemical potential energy input right into the system equates to the sum of the joules the light energy output by the system and also the joules the heat power wasted.
We now define charge, voltage and also current so that we deserve to quantify just how much power is converted to and also from electrical form.

electrical Charge

Opposite fees attract and also like fees repel.

Since antiquity, experimenters have actually noticed that charged objects exert pressures on every other. In fact, objects through opposite charge lure each other and also objects through the same charge repel every other. Us measure charge in devices of coulomb, v symbol C, using positive and negative values to signify its two polarities. The specify name of hopeful and negative was totally arbitrary, but we now recognize that the convention way that electrons are negatively charged.The truth that opposite fees attract and also like charges defeat is why chemistry potential power is needed to separate the hopeful and an adverse charge within the battery in Fig. 1 in order to be convert into electrical energy. It is likewise why electrons circulation from the \$-\$ terminal to the \$+\$ terminal of the battery v the light bulb, and in the procedure convert electrical energy into light and also heat energy.Another empirical observation around charge is that it can not be developed or destroyed. This is stated as conservation of charge: the net fee of a closed device is constant. Because that this reason, the flow of negatively fee electrons is electrically identical to an same amount of confident charge flow in the other direction. Because of the historical an option of electrical polarity, us base the following definitions on the idea of a mobile optimistic charge.
Voltage

A voltage fall is an lot of electric energy per coulomb that charge.

A voltage is a level prefer a elevation is a level. If you litter a record airplane in her apartment, it will probably drop a meter or two before it hits the floor, but if it flies out the window, it could drop much farther. If it flies out the window, gets blown through a gust that wind and also lands over you on the roof, the aircraft has to reduce by a an adverse height. In the same way, a voltage drop relies on its reference point.

Figure 3 Fig. 3: Voltage drop. The voltage fall \$V_1\$ is the autumn in voltage native its \$+\$ label to that is \$-\$ label. We say the \$V_1\$ is the voltage drop across the battery. (We could likewise say that \$V_1\$ is the voltage rise across the battery if we think the the voltage increasing from the \$-\$ label to the \$+\$ label.) as with a drop in height, a voltage drop can be an unfavorable too.
The amount of the voltage fall \$V_1\$ in Fig. 3 is characterized as the joules of electrical energy convert to other develops by \$+1\$ coulomb of fee as it move from the \$+\$ brand to the \$-\$ label with the irradiate bulb. Together a consequence, voltage has units of joules/coulomb (J/C), i m sorry are dubbed volts, with symbol V. In various other words, a \$9 ext V\$ battery can deliver \$9 ext J\$ of power for every \$+1 ext C\$ of charge that moves from its \$+\$ terminal come its \$-\$ terminal.The reality that voltage is identified in state of distinctions in electric energy way that only distinctions in voltage (such as voltage autumn or voltage rises) room meaningful. Later, us will specify a node voltage which shows up to it is in a voltage in ~ a specific location, however even a node voltage is a difference with respect to a reference level referred to as ground.

Current is a measure of how quick charge is moving. Remember that a flow of electron in one direction is tantamount to an same amount of optimistic charge flow in opposing direction. By historic convention, present is defined as the variety of coulombs of confident charge that circulation per second. So, current has systems of coulomb/second (C/s), i beg your pardon are called amperes (or amps), v symbol A.

Fig. 4: present direction. The current \$I_1\$ displayed here is the rate of circulation of confident charge relocating through the light bulb in the direction of the arrow label. Because that example, \$I_1 = 3 ext mA = 0.003 ext A\$ way that \$0.003 ext C\$ of confident charge operation from left to ideal every second. This is the very same as saying that every second about 19 quadrillion \$(19 imes 10^15)\$ electrons with total charge \$-0.003 ext C\$ flow from right to left (in the direction opposite the arrow label). Yet there is no need to fixate top top electrons and also their incomprehensibly large numbers, therefore from now on us will just refer to existing direction in terms of the circulation of optimistic charge.
Even though present direction is characterized with respect to positive charge flow, the value of the present can it is in negative. One easy means to see this is to turning back the arrow label in Fig. 4.
Fig. 5: an adverse current. The present \$I_2 = -3 ext mA\$ means that every 2nd \$0.003 ext C\$ of hopeful charge operation in the direction the opposite the arrowhead label. The is, it flows from left to right, precisely the same as in Fig. 4. This observation makes sense because we have actually not readjusted anything physical. We just reversed the arrowhead label and also (to compensate) changed the sign of the existing value.

A capacitor is a device that separates hopeful and negative charge as soon as a voltage fall is applied across its terminals. The number of coulombs of fee that the separates per 1 volt applied is dubbed its capacitance \$C\$. So, capacitance has units that coulombs/volt (C/V), which are dubbed farads, through symbol F.

Fig. 6: Symbol for a capacitor. The capacitance is \$C\$ and the voltage drop across the capacitor is \$V\$.
If an applied voltage autumn of \$V\$ volts off \$+Q\$ and also \$-Q\$ coulombs of charge from every other, the capacitance is offered byeginalignC=fracQV labelENE-CQVendalignIn this way, a capacitor continues to separate more charge together the voltage distinction increases till the capacitor deserve to no longer withstand the attraction in between the separated optimistic and an unfavorable charges. The voltage drop at this point of break down is dubbed the malfunction voltage.
Fig. 7: A capacitor. This capacitor is labeling as having capacitance the 100 \$mu extF\$ and failure voltage the 63 V.
When a voltage autumn \$V\$ (below the breakdown voltage) is used to a capacitor, electric energy is converted into electrical potential energy that keeps the fee separated. If this voltage difference is permitted to decrease, climate the quantity of fee separated decreases as well, and also so electrical potential energy is converted ago into electric energy. In this way, the capacitor acts as storage for electrical potential energy. If \$C\$ is the capacitance and also \$V\$ is the voltage drop,eginalign extElectrical potential energy stored by a capacitor= frac12CV^2 labelENE-CEQendalignWe can check equation \$eqrefENE-CEQ\$ by verifying that \$(1/2) CV^2\$ has units the joules. Mean \$C=100 ext mu extF\$ and also \$V=63 ext V\$, the capacitance and failure voltage of the capacitor in Fig. 7. Then equation \$eqrefENE-CEQ\$ evaluate toeginalignedfrac12CV^2 &= frac12 (100 ext mu extF) (63 ext V)^2\&= frac12 (100 cdot 10^-6 ext F) (63^2 ext V^2)\&= frac12 (100 cdot 10^-6frac extC extV) (63^2 ext V^2)\&= frac12 (100 cdot 10^-6frac extC extJ/C) (63^2frac extJ^2 extC^2)\&approx 0.2 ext J,endalignedsince \$1 ext F=(1 ext C)/(1 ext V)\$ and \$1 ext V=(1 ext J)/(1 ext C)\$ through definition. This calculation likewise shows that the maximum lot of electric potential power stored through the capacitor in Fig. 7 is 0.2 J (to 1 far-reaching digit).

Batteries room also minimal in the power they deserve to hold. A battery"s fee capacity is regularly reported in milliamp-hours (mA\$cdot\$h) instead of coulombs, because it is practically to think about the capacity as a variety of milliamps the current yielded during a variety of hours.

Fig. 8: A battery pack. This battery load is labeled with a in the name voltage the 3.6 V across its terminals and a nominal fee capacity of 1200 mA\$cdot\$h. Picture source.
We can convert the fee capacity native mA\$cdot\$h come C. Then, we can calculate the energy capacity by noting that the voltage of 3.6 V means that 1 C of fee delivers 3.6 J.eginaligned extCharge volume &= 1200 ext mAcdot exth\&= 1200(0.001 ext A)(3600 ext s)\&= 4320 ext C \ extEnergy volume &= (4320 ext C)(3.6 ext V)\&approx 16000 ext JendalignedTherefore, the battery fill in Fig. 8 can carry out energy of 16 kJ (to 2 far-reaching digits). This amount is approximate because the voltage and also charge capacity values room nominal. In reality, the voltage drop across the terminals is not constant at 3.6 V. It can vary slightly relying on what is associated to the terminals. It also decreases gradually as the power depletes.

For simplicity, we want to stand for a battery-like an equipment that, unlike an yes, really battery, constantly provides a stated voltage drop across its terminals. This best energy resource is called a voltage source and has its own symbol.

Fig. 9: Symbol for a voltage source. This voltage source always provides a voltage drop of \$V_s\$ native the \$+\$ terminal come the \$-\$ terminal, v the terminal labels suggested inside the symbol.
There is another kind that ideal energy source, dubbed a present source, that always drives a specified current through itself. There room no basic devices the act like a existing source, yet the concept is useful for modeling various other devices and also performing circuit analysis.

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Fig. 10: Symbol because that a existing source. This current source always offers a existing \$I_s\$ with optimistic charge flow in the direction that the arrow shown inside the symbol.