Ohm’s Law,Resistance in Series ,Resistance units,Voltage Divider Rule ,Parallel Circuit and Resistan.ce

 

Ohm’s Law

 This law applies to electric to electric conduction through good conductors and may be stated as : The ratio of potential difference (V) between any two points on a conductor to the current (I) flowing between them, is constant, provided the temperature of the conductor does not change. In other words, V I = constant or V I = R where R is the resistance of the conductor between the two points considered. Put in another way, it simply means that provided R is kept constant, current is directly proportional to the potential difference across the ends of a conductor. However, this linear relationship between V and I does not apply to all non-metallic conductors. For example, for silicon carbide, the relationship is given by V = KIm where K and m are constants and m is less than unity. It also does not apply to non-linear devices such as Zener diodes and voltage-regulator (VR) tubes.

what is resistor?

Ans: Resistor is nothing but which opposes the flow of current.

Series Circuits and resistance 

   

 In any Series Circuit Current and Voltage as below  follows:

Current

In a series circuit, the current is the same for all of the elements.

I = I1 = I2 = I3.....= In

Voltage

In a series circuit, the voltage is the sum of the voltage drops of the individual components (resistance units).

Vs=V1+V2+V3+...+Vn

   Resistance in Series 

When some conductors having resistances R1, R2 and R3 etc. are joined end-on-end as they are said to be connected in series. It can be proved that the equivalent resistance or total resistance between points A and D is equal to the sum of the three individual resistances. Being a series circuit, it should be remembered that 

(i) current is the same through all the three conductors

(ii) but voltage drop across each is different due to its different resistance and is given by Ohm’s Law 

 (iii) sum of the three voltage drops is equal to the voltage applied across the three conductors.

           

Resistance units

The total resistance of resistance units in series is equal to the sum of their individual resistances:

Rtotal Rs=R1+R2+R3+...+Rn

Rs = Resistance in series Electrical conductance presents a reciprocal quantity to resistance. Total conductance of a series circuits of pure resistances, therefore, can be calculated from the following expression:

1/Gtotal=1/G1+1/G2

.For a special case of two resistances in series, the total conductance is equal to:

   

    Gtotal = G1G2/(G1+G2)

       

    V = V1 + V2 + V3 = IR1 + IR2 + IR3 +......+ IRn  —Ohm’s Law 

      But V = IR where R is the equivalent resistance of the series combination. 

    ∴ IR = IR1 + IR2 + IR3 or R = R1 + R2 + R3 .

 Voltage Divider Rule 

In electronics, a voltage divider (also called as a potential divider) is a passive linear circuit that produces an output voltage (V_out) that is a fraction of its input voltage (V_in). Voltage division is the result of distributing the input voltage among the components of the divider. A simple example of a voltage divider is two resistors connected in series, with the input voltage applied across the resistor pair and the output voltage emerging from the connection between them.

   

            

     A voltage divider referenced to ground is created by connecting two electrical impedance's in series, as shown in below .The input voltage is applied across the series impedance's  Z₁ and Z₂ and the output is the voltage across Z₂. Z₁ and Z₂  may be composed of any combination of elements such as resistors , inductors and capacitors. If the current in the output wire is zero then the relationship between the input voltage, V_in, and the output voltage, V_out, is:Proving (using Ohm's Law):The transfer function (also known as the divider's voltage ratio) of this circuit is:

Parallel Circuit and Resistance

VoltageIn a parallel circuit, the voltage is the same for all elements.Current The current in each individual resistor is found by Ohm's law. Factoring out the voltage gives.Resistance unitsTo find the total resistance of all components, add the reciprocals of the resistances ${\displaystyle R_{i}}$ of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance:1/Reqa=1/R1+1/R2+1/R3+....1/Rn.For only two resistances, the unreciprocated expression is reasonably simple:This sometimes goes by the mnemonic product over sum.For N equal resistances in parallel, the reciprocal sum expression simplifies to:.and therefore to:.To find the current in a component with resistance ${\displaystyle R_{i}}$, use Ohm's law again:.The components divide the current according to their reciprocal resistances, so, in the case of two resistors,.An old term for devices connected in parallel is multiple, such as multiple connections for arc lamps.Since electrical conductance ${\displaystyle G}$ is reciprocal to resistance, the expression for total conductance of a parallel circuit of resistors reads:.The relations for total conductance and resistance stand in a complementary relationship: the expression for a series connection of resistances is the same as for parallel connection of conductance's and vice versa.
Three resistances, as joined  are said to be connected in parallel. In this case  p.d. across all resistances is the same (ii) current in each resistor is different and is given by Ohm’s Law and (iii) the total current is the sum of the three separate currents. 

                   

       

                         I = I1 + I2 + I3 = V/R1+V/R2+V/R3 

 Now, I = V /R where V is the applied voltage. R = equivalent resistance of the parallel combination. 

∴ V/ R = V/R1+V/R2+V/R3 

1/R=1/R1+1/R2+1/R3  Also G = G1 + G2 + G3 

The main characteristics of a parallel circuit are : 

a. same voltage acts across all parts of the circuit.[Vs=V1=V2=V3]

 b. different resistors have their individual current. [1/R=1/R1+1/R2+1/R3]

c. branch currents are additive[I=I1+I2+I3]. 

d. conductance's are additive.[G = G1 + G2 + G3  ]

 e. powers are additive.