Resistance ㅡ Ohm's Law and Kirchhoff's Laws

DEFINITIONS
resistance - the ability of a substance to prevent or resist the flow of electrical current
Ohm's law - a law stating that the direct current flowing in a conductor is directly proportional to the potential difference between its ends
- {R = V/I} <-- R = resistance in volts/ampere, which is given the derived unit of ohm (Ω)
resistivity - a measure of how strongly a material opposes the flow of current [unit : ohm metre (Ω m)]
gauge number - the number on a wire that measures activity from a radioactive source
series circuit - a circuit in which loads are connected one after another in a single path
parallel circuit - a circuit in which loads are connected side by side
Kirchhoff's current law - "The total amount of current into a junction point of a circuit equals the total current that flows out of that same junction."
Kirchhoff's voltage law - "The total of all electrical potential decreases in any complete circuit loop is equal to any potential increases in that circuit loop."
conservation of electric charge - a law stating that the quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved
conservation of energy - a law stating that the total amount of energy in an isolated system remains constant over time, in other words conserved over time

INFORMATION

16.5 Resistance - Ohm's Law

- the amount of current flow in a circuit, or the amount of energy transferred to the destination, depends on two things:

          1. the potential difference of the power supply (the amount of push)
          2. the nature of the pathway through the loads that are using the electric potential energy

When the pathway becomes more difficult to pass, there is more of a flow of opposition that follows. Ohm's Law also makes intuitive sense if you apply it to the water-and-pipe analogy. If we have a water pump that exerts pressure (voltage) to push water around a "circuit" (current) through a restriction (resistance), we can model how the three variables interrelate. If the resistance to water flow stays the same and the pump pressure increases, the flow rate must also increase; if the pressure stays the same and the resistance increases (making it more difficult for the water to flow), then the flow rate must decrease; and if the flow rate were to stay the same while the resistance to flow decreased, the required pressure from the pump would necessarily decrease.

- In a graph of voltage vs. current, the slope and the V/I ratio represent the resistance of the load because the resistance remains unchanged in the experiment. Having discovered that V/I ratio stays the same for a particular resistor, he came up with the formula of R = V/I, where R is the resistance and given the unit of ohm (Ω).

- It is evident that a thicker wire has a lower resistance than a thinner one because of the the difference in the size of their paths: the broader path in thicker wire makes it easier for current to pass through the load than the narrow path in thinner wire. HOWEVER, there are also other properties of conductors that affect their resistance: its length, cross-sectional area, the material it is made of, and its temperature.



16. 6 Series and Parallel Circuits

- Click here to read about parallel and series circuit

- Resistance in Series:

          R = R1 + R2 + R3

   General Equation:

          R = R1 + R2 + R3 ... + Rx   [x = total number of series resistors in the circuit]

   Resistance in Parallel:

          1/R = 1/R1 + 1/R2 + 1/R3

   General Equation

          1/R = 1/R1 + 1/R2 + 1/R3 ... + 1/Rx [x = total number of parallel resistors in the circuit]

SUMMARY OF EQUATIONS

1. [R = V/I] -- current, resistance, and electrical caution

    R = resistance in ohms (Ω)

    V = voltage/potential difference in volts (V)

     I = current in amperes (A)

2. [R1/R2 = L1/L2] -- resistance / length

    R1, R2 = resistance in ohms (Ω)

    L1, L2 = length in given unit (for example, cm, m, or km)

3. [R1/R2 = A2/A1] -- resistance / cross-section area

    R1, R2 = resistance in ohms (Ω)

    A1, A2 = cross-section area in given unit

4. [R1/R2 = ρ1/ρ2] -- resistance / type of material

    R1, R2 = resistance in ohms (Ω)

    ρ1, ρ2 = resistivity in ohm metres (Ω m)

5. [R = R1 + R2 + R3 ... + Rx] -- resistance in series circuit

    R = total resistance in ohms (Ω)

    R1, R2, R3 = resistances at different parts of the circuit, in ohms (Ω)

    x = the total number of series resistors in the circuit

6. [1/R = 1/R1 + 1/R2 + 1/R3 ... + 1/Rx] -- resistance in parallel circuit

    R = total resistance in ohms (Ω)

    R1, R2, R3 = resistances at different parts of the circuit, in ohms (Ω)

    x = the total number of parallel resistors in the circuit

                                     For more information on Ohm's Law, click here.