## Voltage and Current

#### Voltage and Current

In the domain of electrical elements and systems, voltage and current are our dynamic variables. You can go pretty far in electricity just thinking by analogy with hydraulic systems: voltage is like pressure, and current is like hydraulic flow.

 Domain Generic effort variable Generic flow variable Translational mechanical force (newtons) velocity (meters/second) Hydraulic pressure (newtons/meter2) hydraulic flow (meters3/second) Electrical voltage (volts) current (amperes)

#### Conserved quantity: charge, current

In hydraulic systems, the volume of the incompressible working fluid was a conserved quantity. None of the elements could increase it or decrease it. That had two important consequences:
• Flow was a through variable. Since fluid volume was conserved, the flow rate into one end of any element had to match the amount coming out the other end. So we said there was only one flow in an element, much as there was only one force in a mechanical element.

• -
• By the same reasoning, we arrived at the Junction Rule that the sum of flows into a junction equals the sum of the flows out of that junction.
For electrical systems:
• The conserved quantity is charge, q, measured in coulombs. A coulomb is the charge of about 1019 electrons. A penny contains about 105 coulombs of positive charge -- and exactly the same amount of negative charge.

• -
• The flow variable is current, i, defined as:
• q' = dq/dt = i

• The Junction Rule, also called the Kirchoff Current Law (KCL), states that the sum of currents into a junction equals the sum of currents out of that junction. We will revisit this rule again in the circuit diagrams section.
For hydraulic systems, we tried to restrict ourselves to closed "circuits" in which there was no opportunity for any of our fluid volume to escape (into a "ground lake" or puddle) or to accumulate inside (for instance in an open tank.) That was the sense in which we could say "volume is a conserved quantity". If a system started with 24 liters of fluid distributed within it, it would always contain 24 liters.

For electrical systems this restriction is extremely well obeyed. Even though flows (currents) on the order of many coulombs/second (amperes) may be going on, the total amount of charge, added up in all parts of the system, is effectively zero (typically < 10-9 coulombs or so). Unlike hydraulic fluid volume, charge comes in both positive and negative. (There was no such thing as a negative fluid volume!) The "total volume of electrical fluid" in an electrical circuit is a perfectly balanced zero, but that doesn't deprive the circuit of a working fluid at all.

Current is a through variable. Simple electrical elements have two ends (a.k.a. wires, leads, terminals...) and the current going in one end is the same as that coming out the other end. Current is measured in amperes (nickname: amps). An amp is a colomb/second, and it's measured by an ammeter.

In electricity, you typically hear a lot more about amps than about colombs.

#### Voltage and potential

Voltage is analogous to hydraulic pressure. The unit is volts, and it's measured by a voltmeter.

The electrical term potential is sometimes used in the same sense that we used the hydraulic absolute pressure: you take a one-probe voltmeter and touch various points in a circuit, and say "here the potential is 13 volts, here it is negative seven volts", etc. Unlike absolute pressure, though, potentials can be both positive and negative, and it is debatable whether there is such a thing as a "true zero" potential, in the way that a "true zero" hydraulic pressure can be defined by a perfect vacuum.

What people usually mean by "potential" is the voltage relative to ground. Ground usually really does mean ground (or earth as they call it in Great Britain.) You can stick one probe of your two-probe voltmeter into the mud of the actual planet, and the other you can use to measure the "potential" or "voltage relative to ground" of various points in your circuit. I say usually because sometimes people use a so-called "floating ground" as their common reference point for all potential measurements, and this floating ground may have a non-zero potential relative to the real ground that you, unfortunately, are standing on. The metal chassis inside a TV used to be a 120 volt floating ground about half the time, depending on which way you plugged the TV into the outlet. Ouch! (I guess that's what they meant by "no user servicable parts inside") Making sure that your system's ground is not floating is called grounding it.)

In electricity, you hear a lot more about voltage than potential. Voltage is an across variable. You measure the voltage across a resistor, or a capacitor, etc.

Similar to the"Kirchoff Loop Rule" we used for hydraulic flows, we can sum voltages around a loop in electric systems. The Kirchoff Voltage Law (KVL), states the sum of the voltages added up around any closed loop is zero. We will revisit this rule again in the circuit diagrams section.

#### Power Source: Batteries

The power source we will most often use will be a battery - a constant voltage source. A battery has a rating indicating how many volts it supplies. Here are some common household batteries:
 This 9 volt battery states its rating with its name This is a AA battery - 1.5 volts, capacity of 2600 mAmp-hours This is a D battery - 1.5 volts, capacity of 16500 mAmp-hours
Want to look inside a battery?

Each battery has a positive terminal and negative terminal clearly marked. We know that the voltage jumps across the battery by a value equal to its stated voltage rating. Below is the symbol we will use for batteries in our circuit diagrams, along with the +/- symbols to indicate polarity of the battery, and the direction of current. Note that the wide end of the battery symbol is always the positive side: the +/- symbols are not usually drawn.

If we attach a voltmeter across the battery with the red + lead attached to the + end of the battery and the black - lead attached to the - end of the battery it will read positive. When we apply Kirchoff's Voltage Law to circuits, by convention we will take the voltmeter to be attached to the battery in this way. In general, our current arrow will be drawn sensibly pointing away from the positive end of the battery, and thus using KVL we will usually have a minus sign preceeding the battery voltage in the equation. More on this later...