source of electromotive force A device that, by doing work on charge carriers, maintains a potential difference between its terminals is called a source of electromotive force (emf). Other form of energy is converted into electricity in a source of electromotive force: battery - chemical energy electric generator - mechanical energy solar cell - electromagnetic radiation thermopile - internal energy living cell - chemical energy

electromotive force The maximum electric potential difference that can exist between the terminals of the voltage source is called the electromotive force of that source. I  r + - Voltage produced by a real source of electromotive force:

direct and alternating current If the charge moves in a circuit in the same direction at all times, the current is said to be direct current (DC). Constant current (independent of time) is a special case of direct current. If the charges move (across a surface) changing their direction of motion, the current is said to be alternating current (AC)

circuit analysis Kirchhoff's Junction Rule: The sum of all the currents entering a junction is zero. Kirchhoff's Loop Rule: Around any closed circuit loop the sum of potential differences is zero. I1I1 I2I2 InIn V1V1 V2V2 VnVn

electrical measurements Current is measured with an ammeter, which must be inserted into the circuit in series with the element in which the current is measured. Voltage is measured with a voltmeter, which must be inserted into the circuit in parallel to the elements across which the voltage is measured. The resistance of passive elements can be measured with an ohmmeter. V + - AV ? 

electric current & the human body Currents of 200 mA can be fatal. A current that strong can affect the proper operation of the heart. A current above 100 mA can cause muscle spasm. A person can sense an AC with a current of 1mA. NEVER TOUCH AN OPERATING CIRCUIT WITH BOTH HANDS !!!

inductors An inductor is an element of a circuit with two sides for which (at any instant) the potential difference V between its terminals is proportional to the rate of change in current I passing through this element. I VaVa VbVb The proportionality coefficient L is called the inductance of the inductor. In SI the henry is the unit of inductance

sinusoidal alternating current For a sinusoidal alternating current, both the voltage V(t) across an element and the current I(t) through this element are sinusoidal functions of time. V a (t) V b (t) I (t) V m, I m - the peak value (  t+  ) - the phase  = 2  f - the angular frequency  - the initial phase t V I

electric power t V I P Electric power delivered to an electrical element is a sinusoidal function of time. P av where

AC in the US standard one phase power line The voltage oscillates with frequency f = 60 Hz. 0 V 120 V “ground” “zero” “hot” breaker

AC in the US three phase power line The rms voltage between any "hot" wire and the zero wire is 127 V. Three "hot" wires with phases differing by, the "zero" and the "ground" wires are connected to the outlet. The voltage between any two "hot" wires is 220 V. t V

complex voltage The complex function V (t) such that the voltage across the element is V(t) = Im V (t) is called the complex voltage. Sinusoidal voltage: t V Im V Re V V (t) VmVm t -V m  t+  V

complex current The complex function I (t) such that the current through the element is I(t) = Im I (t) is called the complex current. Sinusoidal current: tt I Im I Re I I (t) ImIm  t+  I t -I m

relation between voltage and current The coefficient Z  relating the peak values of the voltage across the system with the peak value of the current through the system is called the impedance of the system. V m = I m ·Z I V VmVm ImIm tt note that: V rms = I rms ·Z The number   relating the phase of the voltage across the system with the phase of the current through the system is called the phase angle between the current and the voltage  and  V =  I +  

Z complex impedance The complex coefficient Z , relating the complex voltage across an element with the complex current through this element, is called the complex impedance of this element at frequency  : Im Re V I Complex impedance Z includes information about both the impedance Z as well as about the phase angle  Z 

AC in a resistor  R a b I real analysis, impedance and phase angle average power: t V I

AC in a resistor complex analysis  R a b I, complex impedance Z R (  ) = R t V I Im Re ZRZR V I

 L a b I AC in an inductor real analysis, impedance and phase angle average power: t V I =

 L a b I complex analysis t V I complex impedance Z L (  ) = i  L Im Re ZLZL I V,

AC in an capacitor real analysis, impedance and phase angle average power: t V I  C a b I Q -Q