BASIC CONCEPTS OF D.C.CIRCUITS

BASIC CONCEPTS OF D.C.CIRCUITS

➢ ELECTRIC CHARGE

• Amount of current flowing in a conductor is measured in electric charge. 

• Two different kinds of charge, positive and negative.

• It’s denoted by Q or q.

• Electric charge is measured in Columb (c).

➢ VOLTAGE

• We defined voltage as the amount of potential energy between two points on 

a circuit.

• One point has more charge than another.

• This difference in charge between the two points is called voltage. 

• It is measured in volts.

➢ ELECTRIC CURRENT

• The controlled movement of electrons through a substances is called the electric current.

• It is also defined as the time rate of net motion of an electric charge across 

sectional boundary.

I = 𝑄/t

• Coulomb is the SI unit for measurement of electric charge. 

(1 coulomb ≈ 624×1016) and time is measure in second.

• Electric current measure in Ampere.

➢ EMF AND POTENTIAL DIFFERENCE

• Electromotive force (emf) is the force that causes an electric current flow in an electric circuit .
• The potential difference between two points in an electric circuit is that difference in their electrical state which tends to cause flow of electric current between them.

• Volt is a unit of electromotive force as well as potential difference.

➢ RESISTANCE

• Resistance may be defined as that property of substance which opposes the flow of an electric current through it.

• The practical unit of resistance is ohm (Ω).

• For insulators having high resistance, much bigger units Kilo ohm kΩ (10^3) and megohm MΩ (10^6) are used.

• In case of very small resistances smaller unit like Milli ohm (10^−3) and micro ohm (10^−6) are employed.

➢ FACTORS AFFECTING RESISTANCE

• The resistance of wire depends upon its length , area of x- section, type of material, purity and hardness of material of which it is made of and the operating temperature.

• Resistance of a wire is (i)Directly proportion to its length, R 𝛼 l
                                                      (ii)Inversely proportion to its area of x- section,R 𝛼(1/𝑎)
So,  R =ρ(𝑙/𝑎)
Where ρ is a constant depending upon the nature of the material and is known as the specific resistance .

➢ SPECIFIC RESISTANCE

• ρ is a constant depending upon the nature of the material and is known as the specific resistance or resistivity of material of wire. 

                                                                     Or

• Specific resistance or resistivity of material is also defined as the resistance between opposite faces of a unit cube of that material.

• Resistivity is measured in ohm – meter (Ω-m).

➢ CONDUCTOR, INSULATOR AND SEMI CONDUCTOR

• Conductor :
Materials which allow the current to flow easily through them are called the conductor.
• Insulator :
Material which do not allow the current to flow through them are called 
insulator.
• Semi conductor :
Some materials do not allow the current to flow easily through them like conductor and do not oppose the flow of current like insulators. These materials are known as semi conductor.

➢ CONDUCTANCE AND CONDUCTIVITY

• The reciprocal of resistance is called the conductance and denoted by G.

• It is measured in Siemens (s) or mho.
G =1/𝑅=1/(ρ𝑙/𝑎)=(1/ρ)(𝑎/𝑙)=𝜎(𝑎/𝑙)
        Where 𝜎 = (1/ρ) and is known as specific conductance or conductivity of the material.
• Conductivity is the reciprocal of the resistivity

• The unit of conductivity is Siemens/meter (S/m)

➢ OHM'S LAW

• This law applies to electric to electric conduction through good conductors and may be stated as follow:

• The ratio of potential difference (v) between any two points on a conductor to the current (I) following between them, is constant, provided the temperature of the conductor does not change.

V/I= constant R

❑ LIMITATION OF OHM’S LAW

• Ohm’s law can be applied only when temperatures is constant. Because when temperature changes than resistance change.

• Ohm’s law is not applicable to all materials for example semi conductor, silicon carbide etc. they characteristic are not linear.

• Ohm’s law can be applied only A.C. circuits.

➢ EFFECT OF TEMPERATURE ON RESISTANCE

• The resistance of all pure metallic conductors increase with the increase in temperature .

• The resistance of the insulators and non metallic materials generally decreases with the increase in temperature.

➢ RESISTANCE TEMPERATURE CO-EFFICIENT

• Let the resistance of conductor be 𝑅0 at 0℃ and 𝑅1 at 𝑡1℃.

• The rise in temperature becomes (𝑡1- 0) = 𝑡1℃.

• The rise in resistance becomes ∆𝑅 = 𝑅1- 𝑅0.

• Increase in resistance ∆𝑅 depends upon the following factors

(i)It is directly proportional to the value of resistance at initial temperature.

(ii)It is directly proportional to the increase in temperature.

∆R α R0 and ∆R α (t1-0) 

∆R α R0 t1

(R1- R0 ) α R0 t1

R1- R0 = 𝛼0 R0 t1

R1 = R0 +𝛼0 R0 t1

R1= R0 (1 + 𝛼0 t1)                                                                          …….[1] 

Where α0 is constant. Which is known as the resistance temperature co-efficient.

𝛼0= (R1− R0)/(R0 t1)                                                                  …….[2]

➢ VALUE OF 𝛼 AT DIFFERENT TEMPERATURES

• Now let’s get the value of 𝛼0 in the form of 𝛼1 for 𝑡1℃.

• Let the resistance of conductor be 𝑅0 at 0℃ and temperature is increase up to 𝑡1℃.

R1= R0 (1 + 𝛼0 t1)                                                                      …….[3]

Now if we bring it down the same conductor temperature 𝑡1℃ to 0℃.

R0= R1 [1 + 𝛼1 (−t1)]                                                                  …….[4]

R0= R1 (1 − 𝛼1 t1)

R0= R1 − R1 𝛼1 t1

𝛼1=(R1− R0)/(R1 t1)                                                                   …….[5]

But, R1= R0 (1 + 𝛼0 t1)

Put R1value in eq.[5]

𝛼1=[R0 (1+𝛼0 t1) − R0]/[R0 (1+𝛼0 t1) t1]

𝛼1=[R0 + R0 𝛼0 t1 − R0]/[R0 (1+𝛼0 t1) t1]

𝛼1=𝛼0/(1+ 𝛼0 t)                                                                           …….[6]

The value of 𝛼2can be found at any temperature from the value of 𝛼1.

➢ Getting the value of 𝜶2 from 𝜶1

At 𝑡1℃ value of 𝜶 is 𝜶1 and 𝑡2℃ value of 𝜶 is 𝜶2

𝜶1=𝜶0/(1+𝜶0 t)

(1/𝜶1)=(1+𝜶0 t1)/𝜶0

𝜶2=𝜶0/(1+𝜶0 t2)

(1/𝜶2)=(1+𝜶0 t2)/𝜶0

(1/𝜶1)-(1/𝜶2)=(1+𝜶0 t2−1−𝜶0 t1)/𝜶0

(1/𝜶1)-(1/𝜶2)= t2- t1 or (1/𝜶2)=(1/𝜶1)+( t2- t1)

𝜶2=1/[1/(𝜶1)+( t2− t1)]

Let us know the value of resistance R2 on temperature t2. 

(R1/R2)= [R0 (1 + 𝜶0 t1)]/[R0 (1 + 𝜶0 t2)

(R2/R1)=(1+𝜶0 t2)/(1+𝜶0 t1)^-1                                           [(1 + 𝜶0 t1)^−1≈ (1 +𝜶0 t1)]

(R2/R1)= (1 +𝜶0 t2) (1 +𝜶0 t1) 

(R2/R1)= 1 +𝜶0 t2 −𝜶0 t1 − (𝜶0)^2t2t1

(R2/R1)= 1 + 𝜶0( t2− t1)                                                         [(𝜶0)^2t2t1 is negligible ]

R2= R1 [1 + 𝜶0(t2− t1) ]

➢ WORK

• Work is defined as a force causing the movement or displacement of an object.

Work = force × distance

W = F × D

➢POWER

• Power is the rate at which work is done.
• Electric power is expressed in terms of watts .

P = 𝑊/𝑡

➢ENERGY

• Energy is the capacity to do work.

E = power × time

   = p × t

   = V I t

➢ JOULE’S LAW

• According to joule’s law of electric heating, the amount of heat producing in an electric circuit is

Proportional to the square of the current, H 𝛼 𝐼^2

Proportional to the resistance of the circuit, H 𝛼 R

Proportional to the time duration for which the current flow though the circuit, H 𝛼 t.

H 𝛼 I^2 R t

H = (1/J)I^2 R t

Where J is the constant. It’s call joule’s mechanical equivalent .

J = 4.186 joule / kcal

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