Physics 11 : Electrical Symbols and Definitions Basic Concepts

Basic Electricity Vocabulary:

Charge: Charge is the net excess of protons (+) or electrons (-) in an object. Symbol: Q Unit: Coulomb (C) 1 Coulomb = 6.2 x 1018 elementary charges

Electric Current: Current is defined as the rate of flow of positive charge past a point. It is an historical quantity, defined before we knew any details about what charge is, in fact. It is opposite in direction, but equal in magnitude to the “electron flow”, which is the rate of flow of negative charge. Symbol: I Unit: Ampere (A) 1 Ampere = 1 Coulomb per second Equation: I = Q / ∆t

Electric Potential Difference: Also known as voltage, the electric potential difference between any two points in a circuit is the energy difference between those points, per Coulomb of charge passing between the two points. Symbol: V Unit: Volt (V) 1 Volt = 1 Joule per Coulomb Equation: V = ∆E / Q

Simple Circuits:

All circuits must contain a power supply (to provide electric energy), one or more loads (to use that electric energy), and conducting material to connect them (such as copper wire). Many circuits also contain meters (to measure current, voltage, etc.), and control devices (switches, fuses, diodes, etc.)

Ammeters: used to measure current, they are connected in series with another device, so that all the charges traveling through that device must also travel through the ammeter, and be counted.

Voltmeters: used to measure voltage, they are connected in parallel with another device, so that only a tiny bit of the charge is diverted through the voltmeter, and the energy difference per Coulomb of charge is calculated from that sample.

Ohm’s Law:

Conductance: Conductance is the ratio of current produced per unit of voltage through a particular device. It is a measure of how easy it is for charge to travel through that device. Symbol: G Unit: Mho 1 Mho = 1 Ampere per Volt Equation: G = I / V

Resistance: Resistance is the ratio of voltage required per unit of current produced through a particular device. It is the mathematical inverse of conductance, and is a measure of how difficult it is for charge to travel through that device. Symbol: R Unit: Ohm (Ω) 1 Ohm = 1 Volt per Ampere Equation: R = V / I

Rearranging the equation for resistance gives V = I.R and I = V / R. All of these equations are forms of Ohm’s Law. It is most useful for devices which display a constant resistance over a range of applied voltages, otherwise known as “Ohmic devices”. Resistors are Ohmic. Light bulbs are non-Ohmic, since their resistance increases as the voltage increases, and the temperature of the filament increases.

Kirchoff’s Laws:

The circuit shown below has 3 resistors connected in series with one another, and a power source providing a total voltage Vs. The current and voltage measured at each of the three resistors can be predicted using Kirchoff’s Laws for Series Circuits.



Kirchoff’s Current Law for Series Circuits (KCLs): The current through each load in a series circuit is the same as the current provided by the source. Is = I1 = I2 = I3 This is true because every charge leaving the source must also travel through every one of the loads.

Kirchoff’s Voltage Law for Series Circuits (KVLs): The voltage drop across each load in a series circuit adds to the total voltage provided by the power source. Vs = V1 + V2 + V3 This is true because each charge traveling around the circuit gives some of its energy to each one of the loads.

Kirchoff’s Resistance Law for Series Circuits (KRLs): The resistance law for series circuits can be derived from the current and voltage laws. Substituting one form of Ohm’s Law (V=I.R) into the voltage law gives Vs=IsReq(s) = I1R1 + I2R2 + I3R3 Then, since all the current values are the same, dividing both sides by current gives Req(s) = R1 + R2 + R3 The total resistance of a series circuit is larger than any individual resistor value, since every charge must travel through every one of the resistors.

The circuit shown below has 3 resistors connected in parallel with one another, and a power source providing a total voltage Vs. The current and voltage measured at each of the three resistors can be predicted using Kirchoff’s Laws for Parallel Circuits.



Kirchoff’s Current Law for Parallel Circuits (KCLp): The current through each load in a parallel circuit adds to the current provided by the source. Is = I1 + I2 + I3 This is true because the charges being provided by the source divide themselves between the available parallel paths of the circuit.

Kirchoff’s Voltage Law for Parallel Circuits (KVLp): The voltage drop across each load in a parallel circuit is equal to the total voltage provided by the power source. Vs = V1 = V2 = V3 This is true because each charge gives all of its energy to the one load it travels through on its chosen path.

Kirchoff’s Resistance Law for Parallel Circuits (KRLp): The resistance law for parallel circuits can be derived from the current and voltage laws. Substituting one form of Ohm’s Law (I = V / R) into the current law gives

Then, since all the voltage values are the same, dividing both sides by voltage gives

Since the inverse of resistance is equal to conductance, this can also be written as Geq(p) = G1 + G2 + G3 The total conductance of a parallel circuit is larger than any individual load’s conductance, since several circuit paths are now available, each carrying only a fraction of the total charge.

Electric Power and Energy:

Power: Power is defined as the rate at which energy is transferred. In electric circuits, energy is most closely associated with voltage (energy per unit charge). If voltage is multiplied by current (charge per unit time), the result is electric power.

Symbol: P Unit: Watt (W) 1 Watt = 1 Joule per second = 1 Volt.Ampere Equation: P = ∆E / ∆t = V.I

Electric Energy: The electric energy consumed by a device can be calculated by multiplying the power rating by the time used. If you use power in Watts, and multiply by time in seconds, you get energy in Joules, the standard unit. Since this is such a tiny unit, however, it is not commonly used for electric energy - a 40 W light bulb, for example uses 40 J of energy every second. Electric energy is most often quoted in “kiloWatt.hours”, which you get by multiplying power in kiloWatts by time in hours. A kW.h of energy is consumed when you run a 1000 W device for 1 hour.

Symbol: ∆E Unit: Joules (J) or kiloWatt.hours (kW.h) Equation: ∆E = P.∆t or ∆E = V.I.∆t

The cost of running a particular device is determined by the electric energy consumed and the rate charged by the local utility (such as St. Catharines Hydro). Typical rates are around 10 cents per kW.h of electric energy used.