Current Electricity - Part II

2. Electrical resistance and the Ohm’s law
As the electrons flow, they find impediments within the wire material. This impediment is known as resistance. You can visualize that as the current increases, more electrons are flowing. As more electrons start moving, they start colliding with each other and hamper each others speed. The opposition to the flow of charge is known as resistance.

In the experiment with the bulb and the battery, the coil in the bulb is a resistance, it is making the flow of electrons through it slower.

In most electrical circuits, where one wants to use the electric current, like in an electrical appliance, there is always an electrical component called a resistor put in. A resistor is generally made up of carbon or ceramic. It is put in the circuit because it resists the flow of the electric current.

Make a circuit using a few batteries. Connect them to a resistor and an ammeter. Connect a voltmeter across the resistor.  As you change the values of batteries, note down  the voltage developed across the resistor (in volts) and the current flowing in the circuit from the ammeter (in amps). You will see that the voltage and current are directly proportional to each other.  As the voltage increases, the current also increases and vice-versa.

You will notice that

      V
      =  constant
      I

This constant is the measure of resistance in the circuit. To put it more scientifically, electrical resistance is the ratio of the potential difference across an electrical conductor to the current in it. It is denoted as R and the unit of measurement is Ohm (W ).  A resistor and a conductor, the words often mean the same in the context of electrical circuits.

The results seen above was first observed by Ohm and V/I = constant is also known as Ohm’s law. Ohm’s law states that the potential difference between the ends of a conductor is directly proportional to the current flowing in it, provided the temperature and other physical conditions are constant.

Thus                 V
                         =  R
                        I

Resistance in a circuit can be put in series or in parallel, so that their effect can be enhanced or reduced.

Resistance in series : The accompanying circuit diagram shows two resistances R₁ and R₂ connected in series. The total voltage drop across (R₁ + R₂)  is V_.  Measure the voltage drop across R₁, let this be denoted by V₁. Measure the voltage drop across R₂, let this be denoted by V₂.  

Resistance in series

Since the same current I is flowing through both the resistances, we know from Ohm’s Law that

V₁= I x R₁   and V₂= I x R₂

Also V = (V₁ + V₂)  = I  x R_total

Thus we see that

R_total  =  (R₁ + R₂)

Thus for resistances arranged in series, the resultant total resistance is the sum of the individual resistances.

Resistance in parallel : The accompanying circuit diagram shows  two resistances R₁ and R₂ connected in parallel. The voltage drop across both the resistances is V. The current flowing through the circuit is I. But this gets divided into two branches as I₁ and I₂ flowing through R₁ and R₂ respectively.

Resistance in parallel       

I = I₁ +  I₂

But  from Ohm’s law V = I₁ x R₁  and V = I₂ x R₂

Also V = I R_total

                     V                      V                 V
Thus              =            +  
                  R_total                   R₁                    R₂

Hence            1                   1                  1
                    =           +  
                   R_total                R₁                    R₂  

Thus for resistances arranged in parallel, the reciprocal of total resistance is the sum of reciprocal sum of the individual resistances. Thus the resultant resistance is always less that the resistance of any of the resistors itself.

3. Power  
We have studied in earlier chapters that power is the rate of doing work. In current electricity, the word power is used often. It helps us to calculate the electrical energy (or work done) used per unit time.  Power is measured in Watt.

1 watt   = 1 joules per second.

Sometimes a larger unit of watt called kilowatt is used.

1kW  = 1000 watt

To calculate the electrical energy spent while taking a charge of Q coulomb through a potential difference of V volt :

Work done = Q x V
If this work is done in time t then

Power P = Work done/t  = QV/t

From the definition of current I = Q/t

P  = IV 

   =   I²R    (from Ohm’s Law)

In domestic use of electricity, you will see your home electric bill to have written the electrical energy used in kWh or kilowatt- hour. The meters in your home monitor the electrical energy used in your house in terms of kWh. If you buy an electrical equipment, you will note the electrical ratings written on it in terms of kW, higher the wattage, more power is consumed by the equipment. A water heater or a geyser will have an electrical rating of 3kW but a small electric bulb will have wattage of 100 watts only.

Next        Main        Previous