*Notes to a video lecture on http://www.unizor.com*

__Direct Current - Electric Heat__

Consider a circuit with a source of electricity that produces a difference in

*electric potential*(

*voltage*)

*between its terminals. The only other component in this simple circuit is a*

**U**(volts)*resistor*with

*resistance*.

**R**(ohms)According to the Ohm's Law, the electric current going through a resistor is

**I = U/R**(amperes)Recall that a difference in

*electric potential*(

*voltage*) of

*between two terminals of a source of electricity means that it requires one*

**1V**(one volt)*joule*of work (

*) to move one*

**1J***coulomb*of positive electric charge (

*) between these terminals.*

**+1C**Therefore,

*and*

**1V·1C = 1J**

**1V = 1J/1C**Further recall that the electric current of

*is the flow of electricity, when*

**1A**(one ampere)*of electricity is moving across the wire within*

**1C**(one coulomb)*.*

**1sec**(one second)Therefore,

*and*

**1A = 1C/1sec**

**1A·1sec = 1C**In case of our circuit with the voltage between the terminals of a source of electricity

*, electric current*

**U***and resistor*

**I***we have*

**R**

**I***coulombs*of electric charge going through a circuit each

*second*.

So, it

**t***seconds*the source of electricity moves

**I·t***coulombs*of electricity.

Moving one coulomb (

*) of electricity between terminals with one volt (*

**1C***) of a difference in electric potential requires one joule (*

**1V***) of work.*

**1J**Therefore, moving this one coulomb (

*) of electricity between terminals with a difference of electric potential (*

**1C***voltage*)

*requires*

**U**volts*of work.*

**U**joulesContinuing this logic, moving

**I·t***coulombs*of electricity between the terminals with the voltage

*requires*

**U**volts*of work.*

**U·I·t**joulesSo, the work performed by a source of electricity with voltage

*that moves*

**U**(volts)*coulombs electricity every second (*

**I***amperage*) through a resistor with resistance

*during time*

**R**ohms*is (in*

**t**sec*joules*)

**W = U·I·t**From the Ohm's Law

*immediately follows*

**U=I·R***and*

**W = I²·R·t**

**W = U²·t / R**In most cases we will assume that wires have zero resistance and only

resistors have the property of resistance. So, in our simple circuit the

only resistance to the moving electrons is in a resistor

*.*

**R**Since the source of electricity performs work, this work is supposed to

do something. According to the Law of Energy Conservation, the work is

just a transformation of one form of energy into another.

In our case the only result of the work performed by a source of

electricity is moving electrons in a circuit that, meeting resistance of

the atoms inside a resistor, push them around, thus increasing their

chaotic movement inside a resistor. This chaotic movement is

*heat*that can be measured, for example, by measuring a temperature of a resistor.

The bottom line is that a source of electricity that has

*voltage*

*, producing an electric current with*

**V***amperage*

*going through a resistor with*

**I***resistance*

*during*

**R***time*

*performs work*

**t**

**W = U·I·t = I²·R·t = U²·t / R**which is converted to

*heat*that increases the temperature of a resistor.

This process is used in, for example, in incandescent lamps. The rising

temperature of a tungsten spiral inside such a lamp results in heat and

light radiation that lights and heats up the space around a lamp.

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