How resistance relates to potential difference?

To understand what resistance is, it is important to introduce the term: potential difference.

We will elaborate on this a bit later but in short:

  • If we have a circuit with a 12V battery in it, the negative terminal is considered as the reference point (0V).
  • Compared to that negative terminal the positive terminal is at 12V -> it is 12 volts higher.
  • If the current goes through a resistive element (light bulb) there will be a voltage drop across that element. The voltage measured at one end of the bulb and the other differs thus, we can say there is a potential difference across the bulb.

Now we understand that when there is a potential difference it induces current flow from the +ve terminal to the –ve terminal in the wire.

Technically, as we mentioned, before, the electrons flow in the opposite direction (from -ve to +ve and we consider current as the flow of holes – the holes are what electrons leave behind when they are knocked off from their spot by the applied potential difference.

The ride is not smooth for these electrons in the wire as it contains various impurities, defects or other factors such as the natural vibration of the conductor’s crystal lattices. These factors slow down the flow of electrons and act as resistance.

Ohm’s Law

Ohm's Law Equation
  • Rresistance of resistive element (light bulb)
  • Vpotential difference across the resistive element
  • I Direct Current flowing in the resistive element
  • The unit of resistance is Ohm (Ω)
  • Depends on
    • Resistivity (ρ)
    • Dimension of material

According to Ohm’s law (by analysing the equitation): In an ideal conductor, the current is directly proportional to the potential difference.

Conductance

Conductance Equation
  • The inverse of resistance

    • how well does a material conduct
  • Indicated with the symbol G
  • The unit of conductance is siemens (S)
    • Siemens is the same as 1

The 3 Types of Materials

  1. Conductor
    • Low resistance
    • Example: copper – wires are made of copper
  1. Insulator
    • High resistance
    • Example: plastic.
  1. Semiconductor
    • Between conductor and insulator
    • Has special properties – more on this later
    • Example: silicon – used to make transistors

Note: from Ohm’s law: the larger the potential is the more electrons flow thus, the higher the current is. Similarly, with large resistance small current flows.

Ohmic Behaviour:

We can draw the I-V curve for Ohm’s law: The more we increase the voltage (to the right) the higher the current is. Therefore, we see that the current through a conductor is directly proportional to the voltage across it.

Ohmic Behaviour IV Curve
  • Increasing the voltage, the current will increase accordingly in a linear fashion. This means that for example that at higher voltages the current will increase by the same amount as for lower voltages.
  • In an Ohmic behaviour the Resistance is said to be constant: V/I has a constant value at any point along the red line.
  • we assume the temperature and other factors are constant.
  • Example: Metals, carbon

Non – Ohmic Behaviour:

  • In non-linear systems R changes dependent on the voltage applied.
  • So, example in diodes small current flows at low voltages but high current at high voltages.
  • If we take 2 random points along the red curve, V/I for point 1 and point 2 won’t necessarily be the same; thus, it has a non-ohmic behaviour.
  • Example: semiconductors
non-Ohmic Behaviour IV Curve

Resistors

  • They are components and their main job is to control the current
  • Notation: R
  • The current can be controlled from a voltage generator. Voltage generators supply fixed voltage regardless of the current drawn.
  • Rearranging Ohm’s law we get: I=V/R
  • From equation: if V is fixed, by varying R we can increase or decrease I.

Resistors in Series

resistance in series
  • Resistors are in series when we have 2 or more resistors after each other in a circuit
  • The current through both is the same
  • The voltage drop across them depends on the value of the resistor
    • In the above picture V is the voltage drop and the arrows point to the higher potential. Note, the current flows from the left thus, it is the +ve side.
    • If R1=R2 then V1=V2
  • V1+V2= V -> the total voltage drop across both resistors.
resistance in series calculation

When resistors are in series we can simply add them up to get Rtotal.

Resistors in Parallel

resistance in parallel
  • We have 2 resistors in parallel.
  • There is a current I going in that splits up based on the values of R1 and R2.
    • More current goes through the smaller resistance
  • The current is not the same through R1 and R2
  • Meanwhile, the voltage drop is the same across R1 and R2.
resistance in parallel calculation part 1

Now let’s invert the equation:

resistance in parallel calculation part 2

To get Rtotal when resistors are in parallel we have to invert both, add them up and invert the result too.

optional reading: Success in Electronics book by Tom Duncan
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