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Current Electricity – Current, EMF, Ohm’s Law, Resistance

This blog is about current electricity. It covers resistance, temperature dependence of resistance, EMF, Ohm's Law and internal resistance.

9 minutes long
Posted by Mahak Jain, 28/10/2020
Current Electricity – Current, EMF, Ohm’s Law, Resistance

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Modern life can’t run smoothly without electricity, more specifically current electricity. We see several phenomenon relating to current electricity in our everyday life. Lightning is one such phenomenon in which charges flow from the clouds to the earth through the atmosphere. A torch and a cell-driven clock are examples of devices which run via electrical energy. In this blog, we shall study some of the basic laws concerning steady electric currents.

Electric current : What is current in electricity

Charges in motion constitute an electric current.

When a wire is connected to a battery an electric field is set up at every point within the wire. This field exerts a force on each conduction electron. Although, the electrons are continuously accelerated by the field, due to their frequent collisions with the atoms of the wire , they simply drift at a small constant speed in the direction opposite to the field. Thus there is a net flow of charge in the wire at a low rate. The total charge passing through any cross section per second is the electric current in the wire.

Ohm′s Law

The electric current in conductor is proportional to the potential difference between its ends, other factors remaining constant.

                        VαI  ⇒ V=IR

                            R=V/I

where I is the current , V is the potential difference and R is the resistance.

Resistance

The word resistance means opposition. Resistance of the conductor is the opposition offered by the conductor to the flow of electron passing through it. It depends on material of the conductor and dimensions of the conductor 

                          R=ρL/A

        where , ρ is resistivity of material

                    L is length of conductor 

                    A is uniform cross sectional area

              ρ=1/σ, σ is conductivity of material

Resistivity depends on the properties of the material and on temperature. Resistivity is a property of a substance and resistance is property of an object.

Dependence of Resistance on various factors

                       R α L/A 

   As we know Volume =Area x length

                       R α L² /V

                     ⇒ R α L²

                 or      R α 1/A²

  • If we reduce the thickness of the wire, resistance increases because electrons don’t have as much space to flow down the wire.
  • If we increase the length of wire resistance increases because electron has to deal more friction from the side of the wire. 

for example –

If a wire stretches to double its length, then what is the new resistance if the original resistance of the wire was R?

                      L₁=L, L₂=2L 

                      R₁=R , R₂=? 

    as we know , R α L²

                      R₁/R₂=L²₁/L²₂

                      R²/R₂= L²/4L²

                            R₂= 4R

Therefore, if a wire stretches to double its length, new resistance is 4 times the original resistance

Temperature dependence of Resistance –

As discussed earlier, resistance of a conductor depends on its length and area of cross section. As temperature changes the length and area also change. When the temperature of a material increases up it becomes hotter this is because atoms are vibrating more vigorously and bouncing off each other and giving off heat energy. The quicker the atoms move the more difficult it is for electrons to get to where they want to go to.

             R(T)=R(T₀)[1+α(T-T₀)+β(T-T₀)²]

where both α and  β are temperature coefficient of resistance. R(T) is resistance at temperature T, R(T₀) is resistance at temperature at T₀ .

        β is negligibly small for pure metals ,so the resistance varies linearly with the temperature.

                R(T)=R(T₀)[1+α(T-T₀)]

  • Temperature coefficient α is constant for given material. This temperature coefficient α is positive for metals ( for example , α for Cu is 0.004 per degree). That is why for good conductors an increase in temperature will result in an increase in the resistance level.
Resistance temperature curve
  • In case of alloys such as manganin and nichrome, it is very small (almost zero).
  • For semiconductor materials, an increase in temperature will result in a decrease in the resistance level. Consequently, semiconductors have negative temperature coefficient. 

Validity and failure of Ohm’s law

   Ohm’s law is not a universal law . It doesn’t apply everywhere under all conditions. Under normal working temperature metallic conductors obey Ohm’s Law. Thus, are called Ohmic conductors . Even Ohmic conductors do not follow this law at very high currents or voltages.

Semiconductors also do not follow Ohm’s law as shown in the figure.

  • Materials not obeying Ohm’s law are – 
  1. Vacuum tubes 
  2. Superconductors
  3. Thermistor 
  4. Transistors 
  • Conditions responsible for failure of Ohm’s law
  1. Very High temperature
  2. Too low temperature
  3. Very high potential difference

EMF and Battery (source of current electricity)

Battery is a device which maintains a potential difference between its two terminals. It exerts force on the charges present inside the battery material by some internal mechanism .

EMF and Battery source of current electricity

Positive charges move towards A terminal of battery and negative charges move towards B terminal of battery due to this battery force F(b). As positive charges accumulate on A terminal and negative charges accumulate at B terminal, a potential difference develops between these two terminal of battery .

The work a battery does in pushing the positive charges from its negative terminal to its positive terminal through a distance L with a force F(b) is given by

             W=F(b)L=F(el)L=qE(el)L=qV(b)

Then , the work done per unit charge is                          

                              W/q=V(b)

This is electromotive force of the battery (E) , E = W/q 

Internal Resistance Of a Cell

– Results in loss of electricity

Potential difference in a circuit is not equal to the emf of battery. This is because charge moving through the material encounters resistance. This resistance of battery named as internal resistance of battery denoted by r. According to Ohm’s law r is constant and it doesn’t depend on current I. If current flown through circuit is I, then the potential difference between the terminal of the source is V = E – Ir. EMF is independent of the resistance of the circuit and depends upon the nature of electrolyte of the cell, while potential difference depends upon the resistance between the two points of the circuit and current flowing through the circuit.

Potential difference across the terminals of cell in different situations-

Internal resistance of a cell

  1 .Discharging of a battery –

  Direction of current – negative terminal to positive terminal 

             V(A)-V(B) = E- Ir

                  V(AB) <E 

  2. Charging of a battery –

  Direction of current – positive terminal to negative terminal 

                 V(A)-V(B)= E+ Ir 

                        V(AB)>E

   3. Battery is open circuited- 

            Current I = 0 

                  V(AB) = E

   4. Battery is Short Circuited-

                     V=0 

                  E- Ir = 0 

                    I=E /r


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