The term DC means direct current. A DC circuit has current flowing in only one direction and is usually powered by a battery. The principle circuit elements are:
name


variable


unit

symbol

source of emf 

ε

volts 
V 

resistor 

R 
ohms 
Ω


wires 





switch 





ammeter 


amperes 
A 

voltmeter 


volts 
V 

When a switch is closed in a DC circuit, charges in the wire do NOT instantaneously start moving at the speed of light. Closing the switch merely declares a direction of high to low potential  it establishes an electric field in the circuit. Consider the following analogy.
A crowd of people are milling around in the lobby prior to the beginning of a play. Some are standing still, some are circulating to visit friends or find refreshments, others are just randomly strolling to stretch their legs. Then, the bell rings to state that the audience has five minutes before the second half of the play is to begin. At that moment, the crowd now has a preferred direction of motion, out of the lobby (high potential) to their seats (low potential). No one person in the crowd instantaneously pops into his seat, everyone begins to drift in the "circuit's" prescribed direction of flow. Each person's drift velocity is small, although the instantaneous result of the bell is that seats start filling up in preparation for the curtain's rising.
A switch does the same thing as the bell, it tells the charges which direction they are to flow. No one charge moves at the speed of light, all charges begin drifting towards positions of lower potential thus causing a current in the circuit. The average drift velocity of charges in an electric circuit is on the order of a few centimeters per second. As soon as the switch is opened again, the electric field is removed, and the charges once again randomly move in all directions through the wire canceling out any net flow.
Before practicing with circuits that have one or more resistors, we need to look at some fundamental relationships between volts, ohms, amperes, and watts.
Ohm's Law: V = IR
This law can apply to individual resistors, combinations of resistors or to an entire circuit. The variables in this formula stand for:
potential difference 
V 
volts 

V = J/C 
current 
I 
amperes 

A = C/sec 
resistance 
R 
ohms 

Ω = Jsec/C^{2} 
Joule's Law: P = IV
This law relates the power dissipated through a resistor to its current and voltage. The variables in this formula stand for:
power 
P 
watts 

watt = J/sec 
current 
I 
amperes 

A = C/sec 
potential difference 
V 
volts 

V = J/C 
By substituting in variations of Ohm's Law, this formula can be rewritten as:
P = IV P = I(IR) →
P = I^{2}R
P = (V/R)V →
P = V^{2}/R
These variations allow you flexibilty in how you calculate the power dissipated through a resistor.
Power, which is defined as the rate at which work is done or energy is used, is measured in watts [1 watt = 1 J/sec]. This quantity is CONSERVED in circuits; that is, the power supplied by the battery must be equal to the power consumed by all of the resistors in the circuit. Sometimes problems will ask you to calculate power by asking for "the rate at which heat [i.e. energy] is dissipated through a circuit element."
Rearranging this equation gives us another often used expression, Pt = Energy.
In mechanics, you were sometimes asked to calculate the power required for a constant force to move an object at a constant velocity; for example, the power required by an airplane's engine to maintain a plane's constant forward velocity or the power required to lift a mass on the end of a string at a constant rate. In this instance, power was calculated with the equation P = Fv.
Power = Work/time
Power = Fs/t = F(s/t) = Fv
Resistance of a wire: R = ρ(L/A)
This law relates the resistance of a wire to the material from which it is composed, its resistivity, its length, and its crosssectional area. The variables in this formula stand for:
resistance 
R 
ohms 

Ω = Jsec/C^{2} 
resistivity 
ρ 
rho 

ρ = Ωm 
length 
L 
meters 

m 
area 
A 
square meters 

m^{2} 
Details of the relationships in this formula will be discussed in a later lesson called "Filaments and Power." Combinations of Resistors: Series Circuits
The formulas used to calculate the equivalent resistance, voltage and current through a collection of three resistors wired in series are:
R_{eq} 
= 
R_{1} + R_{2} + R_{3} 
V_{eq} 
= 
V_{1} + V_{2} + V_{3} 
I_{eq} 
= 
I_{1} = I_{2} = I_{3} 
Note that we will be considering the wires in our examples to have negligible resistance and will not be treating them as resistors; although in real circuits, the length, diameter, and resistivity of the conducting wires are critical components in a circuit.
