## Electricity, the basics:

Electricity in wired circuits consists of the flow of electrons.

Current is the word used to describe this flow, and is measured in amperes.

Because positive and negative charge "dislike" being apart, current can only flow when a complete circuit exists: At least one closed loop for the electrons to run around.

A Simple Circuit

Current flows because of an electric potential—voltage—that exists in the circuit. An example of a source of voltage is a battery; here electrochemical reactions produce electric potential. Another example is a power generator powered by steam (a turbine) or by rushing water (hydroelectric generators). The former are examples of constant (DC) voltage sources (most flashlight batteries produce a constant 1.5 volts) and the latter AC sources, where the voltage varies sinusoidally.

AC voltage is what wall sockets provide,with the voltage given by the formula

v(t) = 110*÷2 sin (2p 60 t)

Amplitude = 110*÷2 volts

Frequency = 60 Hz

Circuits are comprised of connected elements. Each element is distinguished by the relation it imposes on the voltage across it and the current flowing through it.

Electrical engineers frequently use combinations of these ideal circuit elements to describe the behavior of real ones.

Circuit Elements

* The voltage source produces a DC or AC voltage, and does so regardless of the current flowing through it.

* A straight line indicates a wire that has no voltage drop across it and allows current of any size to flow through it. Wires are used to interconnect circuit elements to form circuits.

* A resistor constrains its voltage and current to be proportional. This relation amounts to the most famous circuit law: Ohm's Law.

V = RI

R - resistance in ohms (W)

V - voltage (volts)

I - current (amperes)

* A capacitor is the charge storage device. The charge stored in a capacitor is proportional to the voltage across it.

Q = CV

Q - charge in coulombs

C - capactiance (farads)

V - voltage (volts)

* Because the rate of change of charge is current, the relation between current and voltage in a capacitor is I = C dV/dt.

A switch opens and closes a connection according to some external influence. Thus, a switch models the opening and closing of a telegraph switch by an operator. When open, no current flows and any voltage can be present across it. When closed, any current can flow through it and no voltage drop occurs (it acts like a wire).

Real wire has resistance; for wire of length L and cross-sectional area A

(since wire is usually circular, A = pd2/4, d = wire diameter), its resistance is

R = rL/A

r - resistivity (W-cm)

The resistivity of common conductors

Resistivity (W-cm) for Common Metals at Room Temperature Aluminum 2.828 x 10-6

Copper 1.676 x 10-6

Silver 1.586 x 10-6

Gold 2.214 x 10-6

Tungsten 5.510 x 10-6

For example, a 10 Gauge wire is 2.588mm in diameter.

The resistance per cm of copper wire that thick is 3.186 x 10-5W/cm.

A mile of this wire has a resistance of 5.13 W.

Current is the word used to describe this flow, and is measured in amperes.

Because positive and negative charge "dislike" being apart, current can only flow when a complete circuit exists: At least one closed loop for the electrons to run around.

A Simple Circuit

Current flows because of an electric potential—voltage—that exists in the circuit. An example of a source of voltage is a battery; here electrochemical reactions produce electric potential. Another example is a power generator powered by steam (a turbine) or by rushing water (hydroelectric generators). The former are examples of constant (DC) voltage sources (most flashlight batteries produce a constant 1.5 volts) and the latter AC sources, where the voltage varies sinusoidally.

AC voltage is what wall sockets provide,with the voltage given by the formula

v(t) = 110*÷2 sin (2p 60 t)

Amplitude = 110*÷2 volts

Frequency = 60 Hz

Circuits are comprised of connected elements. Each element is distinguished by the relation it imposes on the voltage across it and the current flowing through it.

Electrical engineers frequently use combinations of these ideal circuit elements to describe the behavior of real ones.

Circuit Elements

* The voltage source produces a DC or AC voltage, and does so regardless of the current flowing through it.

* A straight line indicates a wire that has no voltage drop across it and allows current of any size to flow through it. Wires are used to interconnect circuit elements to form circuits.

* A resistor constrains its voltage and current to be proportional. This relation amounts to the most famous circuit law: Ohm's Law.

V = RI

R - resistance in ohms (W)

V - voltage (volts)

I - current (amperes)

* A capacitor is the charge storage device. The charge stored in a capacitor is proportional to the voltage across it.

Q = CV

Q - charge in coulombs

C - capactiance (farads)

V - voltage (volts)

* Because the rate of change of charge is current, the relation between current and voltage in a capacitor is I = C dV/dt.

A switch opens and closes a connection according to some external influence. Thus, a switch models the opening and closing of a telegraph switch by an operator. When open, no current flows and any voltage can be present across it. When closed, any current can flow through it and no voltage drop occurs (it acts like a wire).

Real wire has resistance; for wire of length L and cross-sectional area A

(since wire is usually circular, A = pd2/4, d = wire diameter), its resistance is

R = rL/A

r - resistivity (W-cm)

The resistivity of common conductors

Resistivity (W-cm) for Common Metals at Room Temperature Aluminum 2.828 x 10-6

Copper 1.676 x 10-6

Silver 1.586 x 10-6

Gold 2.214 x 10-6

Tungsten 5.510 x 10-6

For example, a 10 Gauge wire is 2.588mm in diameter.

The resistance per cm of copper wire that thick is 3.186 x 10-5W/cm.

A mile of this wire has a resistance of 5.13 W.