Voltage, current, and generic circuit elements

We know that information can be represented by signals; now we need to understand how signals are physically realized. Over theyears, electric signals have been found to be the easiest to use. Voltage and currents comprise the electric instantiationsof signals. Thus, we need to delve into the world of electricity and electromagnetism. The systems used to manipulate electricsignals directly are called circuits , and they refine the information representation or extract informationfrom the voltage or current. In many cases, they make nice examples of linear systems.

A generic circuit element places a constraint between the classic variables of a circuit: voltage andcurrent. Voltage is electric potential and represents the "push" that drives electric charge from one placeto another. What causes charge to move is a physical separation between positive and negative charge. A battery generates,through electrochemical means, excess positive charge at one terminal and negative charge at the other, creating an electricfield. Voltage is defined across a circuit element, with the positive sign denoting a positive voltage dropacross the element. When a conductor connects the positive and negative potentials, current flows, with positive current indicating that positive charge flows from the positiveterminal to the negative. Electrons comprise current flow in many cases. Because electrons have a negative charge, electronsmove in the opposite direction of positive current flow: Negative charge flowing to the right is equivalent to positivecharge moving to the left.

It is important to understand the physics of current flow in conductors to appreciate the innovation of new electronic devices. Electric charge can arise from many sources, thesimplest being the electron. When we say that "electrons flow through a conductor," what we mean is that the conductor'sconstituent atoms freely give up electrons from their outer shells. "Flow" thus means that electrons hop from atom to atomdriven along by the applied electric potential. A missing electron, however, is a virtual positive charge. Electricalengineers call these holes , and in some materials, particularly certain semiconductors, current flow is actuallydue to holes. Current flow also occurs in nerve cells found in your brain. Here, neurons "communicate" using propagatingvoltage pulses that rely on the flow of positive ions (potassium and sodium primarily, and to some degree calcium) across theneuron's outer wall. Thus, current can come from many sources, and circuit theory can be used to understand how current flowsin reaction to electric fields.

Generic circuit element

Current flows through circuit elements, such as that depicted in [link] , and through conductors, which we indicate by lines in circuit diagrams. For everycircuit element we define a voltage and a current. The element has a v-i relation defined by the element's physical properties. In defining the v-i relation, we have the convention that positive current flows from positive to negative voltage drop. Voltage has units ofvolts, and both the unit and the quantity are named for Volta . Current has units of amperes, and is named for the Frenchphysicist Ampère .

Voltages and currents also carry power . Again using the convention shown in [link] for circuit elements, the instantaneous power at each moment of time consumed by the element is given by the product of the voltage and current. $$p(t)=v(t)i(t)$$ A positive value for power indicates that at time $t$ the circuit element is consuming power;a negative value means it is producing power. With voltage expressed in volts and current in amperes, power defined this way has units of watts . Just as in all areas of physics and chemistry, power is the rate at which energy is consumed or produced. Consequently, energy is the integral of power. $$E(t)=\int_{()} \,d \alpha$$∞ t p α Again, positive energy corresponds to consumed energy and negative energy corresponds to energy production. Note that a circuit element having a power profile that is both positive and negative over some time interval could consume or produce energy according to the sign of the integral of power.The units of energy are joules since a watt equals joules/second.