Circuits - I


 Recall the definition of Voltage:

Voltage (V) - the amount of available energy per coulomb of charge.  The unit is the joule per coulomb, called a volt (V, in honor of Allesandro Volta, inventer of the battery).

V = E/Q


Batteries and other sources (such as wall sockets) "provide" voltage, which is really a difference between TWO points (marked + and - on a battery).  




Or in schematic form:




We also need to quantify the rate at which charge can flow.  For mathematical simplicity, we assume that positive charge is "flowing".  We call this flow rate "current".


Current (I) - the rate at which positive charge "flows"

I = Q/t

The unit is the coulomb per second, defined as an ampere (A).  Just as one coulomb is a huge amount of charge (nearly 6.3 billion billion protons), one ampere (or amp) is a tremendous amount of current - more than enough to kill a person.  In fact, you can feel as little as 0.01 A.  Typical currents in a circuit are on the order of mA (milliamperes).

Essentially, current is how quickly charge travels (or charge per time, q/t).  The unit (a coulomb per second) is called the ampere (or amp, A).  To keep things simple, we think about positive charge moving, even though it is really all about the electrons.




We also need to quantify how much something slows down current.  This is called resistance.

Resistance (R) - the ratio of voltage applied to an electrical device to the current that results through the device.  Alternately:  the amount by which the voltage is "dropped" per ampere of current.

R = V/I

You can also think of resistance as that which "resists" current.  Typically, resistors are made of things that are semi-conductive (they conduct current, but less well than conductors and better than insulators).  Resistors are often made of carbon, but can also be made of silicon and other materials.  The unit is the volt per ampere, defined as an ohm (Greek symbol omega)

A convenient way to relate all of the variables is embodied in an expression often called Ohm's Law:

V = I R
Resistors are common electrical components, usually represented by a jagged line or a box.




So, what exactly IS a circuit?

An electrical circuit can be thought of as a complete "loop" through which charge can travel.  Therefore, it actually has to be physically complete - there can be no openings.  That is, the current actually has to have a complete path to take.  I will demonstrate this in class with bulbs and wires; for now, see the image above.

Some folks like analogies.  Consider a water analogy.  Voltage is like a tank of water (how much water).  Resistance is provided by a drain or faucet.  The rate at which water comes out is the current.  It's only an analogy, but it gets the gist of circuit terminology ok.


Power


What about power?

Also consider electrical power (P).  Power is the rate at which energy is used or expended:  energy per time.  Symbolically:  P = E / t.  The unit is the joule per second, called a watt (W).  In electricity, power is also given by:
P = I V
P = I^2 R


Power allows us to express the brightness of a bulb.  Consider that a 100-W bulb is brighter than a 60-W bulb.

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