Resistance, Conductance, and Types of resistor
Resistance
Resistance is the ability of a material to resist the flow of current. It is represented by the symbol ‘R’. S.I unit of resistance is Ohm (Ω). Electrical resistance is implemented by a two-terminal passive element in a circuit called a resistor.
Why resistance occurs in a material (wire)?
An electric current flows when electrons move through a conductor, such as a metal wire. The moving electrons can collide with the ions in the metal. This makes it more difficult for the current to flow and causes resistance.
Factors on which resistance of a conductor depends
- Length of conductor: The resistance of a conductor or resistor is directly proportional to the length of material in direction of the current. As length increases electrons collide with more ions as they pass through.
- The cross-sectional area of the conductor: The resistance of a conductor is indirectly proportional to the cross-sectional area of the conductor. As the cross-sectional area increases the number of electrons to carry the current increases. So, the resistance of the conductor decreases.
- The material of the conductor: Resistance of the conductor also depends on the material by which the conductor is made.
- The temperature of the conducting material: Click here to know in full detail.
\[R \propto l \\ R\propto \frac{1}{A} \\ \Rightarrow R \propto \frac{l}{A} \Rightarrow R = \rho \frac{l}{A} \]
- R=Resistance of a conductor.
- l=Length of a conductor in the direction of current flow.
- A=The cross-section area of the conductor.
- ρ=Resistivity of a material by which conductor is made.
Resistivity
Resistivity is the fundamental property of a material to resist the flow of current. S.I unit of resistivity is ohm-meter (Ω-m). It is represented by ρ. The value of resistivity varies from material to material.
The resistivity of a material also depends on the temperature of that material. We will discuss it in another article.
From Ohm’s law, we know that V=IR; where V is the voltage across the element, I is the current through that element, and R is the resistance of that electrical element.
\[R= \frac{V}{I} \Rightarrow \rho \frac{l}{A} = \frac{V}{I} \\ \rho = \frac{ \frac{V}{l} }{ \frac{I}{A} } = \frac{E}{J} \\ \rho = \frac{E}{J}
\]
In the above equation, ρ is the resistivity of the conductor material, E is the magnitude of electric field and J is the magnitude of current density.
This expression of resistivity is used when the current and electric field varies in different parts of the material. Here, resistivity at a particular point is defined as the ratio of the electric field to the density of current at a point.
Conductivity and conductance
Conductivity
Conductivity is the inverse of resistivity. It is the property of a material to allow the flow of current. It is denoted by σ. It also depends on the material of the conductor.
\[ \sigma = \frac{1}{ \rho } = \frac{1}{\frac{E}{J}} = \frac{J}{E}
\]
Conductance
Conductance is the inverse of resistance. It is the ability of an electrical element to conduct electric current through it. It is denoted by G.
Formulas for conductance:
\[G= \frac{1}{R} = \frac{1}{ \rho } \frac{A}{l} = \sigma \frac{A}{l}\\ G= \sigma \frac{A}{l} \\ or\space R= \frac{V}{I} \Rightarrow G= \frac{1}{R} = \frac{I}{V} \]
S.I unit of conductance is mho or Siemens denoted by inverted omega(℧).
Power dissipated by a resistor or conductor
In terms of resistance (R)
\[P=vi=iR \times i= i^{2} R= \frac{ v^{2}}{R} \]
In terms of conductance (G)
\[P=vi=v \times Gv= v^{2} G= \frac{ i^{2}}{G} \]
From above equations following point to be noted:
- Power dissipated in a resistor is non-linear function of either current or voltage.
- Since R and G are positive quantities, the power dissipated is always positive. Thus a resistor always absorbs power from the circuit which satisfies passive sign convention and proves resistance is a passive element.
Types of resistors
Linear Resistor
A resistor that obeys ohm laws is called a linear resistor. It has constant resistance and thus v-i characteristic is a straight line passing through the origin. Its resistance does not vary due to changes in current, voltage, temperature, or any other thing. Linear resistor further classified into the fixed resistor and variable resistor.
Fixed Resistor
Most of the resistors are of the fixed type which means their resistance is constant. An ideal fixed resistor provides constant resistance with the change in voltage, temperature, or frequency. However, the resistance of the practical resistor varies slightly with an increase in temperature. In practice no resistor is perfect and all resistors have a certain stray capacitance and inductance resulting in an impedance value different from the nominal value of resistance.
The most frequently used resistance values of the fixed resistors include 100kΩ, 10kΩ, 1000Ω, 10Ω.
The cost of fixed resistors is high when compared to the cost of variable resistors because each time we change resistance we have to buy a new fixed resistor. While in the case of a variable resistor we use a single resistor for different values. Let us discuss some examples of fixed resistors.
Carbon composition resistor
The composition resistor is used when large resistance is needed. The carbon composition resistors are made from a cylindrical resistive element with embedded metal end caps. The cylindrical resistive element of the carbon composition resistor is made from a mixture of carbon powder, graphite, and ceramic dust mixed with a binder substance like clay. The carbon powder acts as a good conductor of electricity.
- The thermal mass of the carbon composition resistor is higher so as to withstand high-energy pulses.
- These resistors have low stability and high noise which is a disadvantage.
- These are used in surge protection, current limiting, and high voltage power supply.
Wire wound resistor
The wire-wound resistor is made by winding the metal wire around a metal core. The metal wire conducts electricity but has a certain resistance. While the metallic core acts as the non-conductive material.
- Normally a manganin or a nichrome wire is used to wind the core because they offer high resistance. Whereas plastic, ceramic, or glass is used for the core.
- Wire wound resistors are very acurate.
- They work excellently for low resistance values and high power ratings.
- These are the oldest type of fixed resistors but are being used even now.
Variable resistor
Variable resistors are those resistors in which we can change or adjust the value of resistance. Most variable resistors are adjusted by mechanical movement(linear or rotatory). Potentiometer, rheostat, and trimmers are some examples of variable resistors.
Potentiometer
The potentiometer is a three-terminal element with a sliding contact or wiper which s used for controlling the voltage in the circuit. The resistance between the two fixed terminals is constant while the third terminal is connected with a moving wiper which is variable. By sliding the wiper the resistance between the wiper terminal and fixed terminal vary.
Non-Linear Resistor
A non-linear resistor does not obey ohm’s law. Its resistance varies with current. For example light bulbs, thermistors, varistors, etc.