Dr. D. Y. Patil Institute of Engineering Management and Research Akurdi Pune-411044

ELECTRICAL ENGINEERING SECTION

MODEL ANSWERS

BASIC ELECTRICAL ENGINEERING

UNIT 1

UNIT 1

Q1.Define Insulation resistance & obtain an expression for insulation resistance of a single core cable.

Q2. With usual notations: derive the relationship, α 2=α 1

1+α 1 ( t 2−t 1 ) & hence obtain

1) α t=α0

1+α 0 t 2) α 0=α t

1−αt tQ3.Define temperature coefficient of resistance. State its unit & the factors on which it depends.

Q4. Explain the effect of temperature on resistance of 1) Metal Conductors 2) Insulators 3) Alloys.

UNIT 1

Q1.Define Insulation resistance & obtain an expression for insulation resistance of a single core cable (6 Marks)[Dec-13,May13,May15]

Ans:- Insulation resistance:- It is defined as the resistance offered by an insulator to the flow of leakage current. This insulator try to avoid any leakage of current from the current carrying conductor to the earth. It is denoted by Ri & Mathematically can be given as,

Ri= V/ I1

where, V= Voltage measured between conductor & earthI1= Leakage currentRi = Insulation Resistance

Expression for insulation resistance of a single core cable:-Fig shows a cable in which the inner conductor is completely covered by a layer

of insulating materials.

Fig Insulation Resistance

Consider a conductor which is completely covered by layers of insulating material. In such cable the leakage current flow in a outward direction from conductor. Hence cross section of a path of current is not constant but continuously changes along its length.

Consider a cross section of a cylinder cable of a radius ‘r’ with a small thickness of ‘dr’If the length of a cable is ‘l’ then its area perpendicular to the flow of current having surface area 2πrl.Thus the total insulation resistance for Ri can be given by,

Ri=∫R 1

R 2

dRi

¿∫R 1

R 2 ϱdr2 πrl

¿ ϱ2 πl∫R 1

R 2 drr

= ϱ2 πl

¿

∴ Ri = ϱ2πl [loge R2- loge R1]

∴Ri=2.303 ϱ2πl

log10( R2

R1)Ω

This is the expression for insulation resistance

where R1= radius of the conductor

R2 = Radius of the cable including the conductor & insulator.

Q2. With usual notations: derive the relationship, α 2=α 1

1+α 1 ( t 2−t 1 ) & hence obtain

1) α t=α0

1+α 0 t 2) α 0=α t

1−αt t (6 Marks)(May 14)

Ans :- Resistance Temperature Coefficient: It is defined as ratio of change in resistance per degree rise in temperature to the initial resistance.

Let Rt 1∧Rt 2 be the resistance of a conductor at t 10C & t 2

0C respectively, & α t 1 & α t 2 be the corresponding temperature coefficients.

Suppose the conductor is heated from one initial temperature t 10C to a final temperature t 2

0C .

Fig: Variation of Resistance with Temperature

Then by definition of RTC

Rt 2 = Rt 1[1+α t 1 (t2-t1)] ---------------------- Eq. 1

The same conductor is now cooled from t 20C to t 1

0C .

Rt 1 = Rt 2[1+α t 2 (t1-t2)] ---------------------- Eq. 2

Substituting equation 2 in 1

Rt 2= Rt 2[1+α t 2 (t1-t2)] [1+α t 1 (t2-t1)]

1 = [1+α t 2 (t1-t2)] [1+α t 1 (t2-t1)]

= [1- α t 2 (t2-t1)] [1+α t 1 (t2-t1)]

11+αt 1 (t 2−t 1 ) = 1- α t 2 (t2-t1)

α t 2 (t2-t1) = 1 - 1

1+αt 1 ( t 2−t 1 )

= 1+αt 1 ( t 2−t 1 )−1

1+αt 1 ( t 2−t 1 )

= α t 1 ( t 2−t 1 )

1+αt 1 ( t 2−t 1 )

α t 2 = α t 1

1+αt 1 (t 2−t 1 )

This expression shows the effect of temperature on α i.e. R.T.C

Where α 2= R.T.C at temp. t 20C α 1= R.T.C at temp. 0C

(t2-t1) = Temperature difference

If we substitute t1 =00C & α 1=¿ α 0then we get R.T.C at any temp. in terms of R.T.C. at 00C i.e α 0as ,

α t=α0

1+α 0 t ------------------Eq. 3

Rearranging we get, α t+αt α 0 t= α 0

∴αt=α 0(1- α t t)

∴ α 0=α t

1−αt t ---------------------- Eq. 4

Q3. Define temperature coefficient of resistance. State its unit & the factors on which it depends (6 Marks ) [Dec-14]Ans. Temperature coefficient of resistance:- It is defined as ratio of change in resistance per degree rise in temperature to the initial resistance

Fig : Resistance Temperature Coefficient

It is given by, α0 =( Rt – R0)/ R0 ×Δt & Its Unit is “/0 C” (per degree Celsius) where R0 – Resistance at 00 C Rt – Resistance at t0C Δt= rise in temperature

It is dependent upon following factors:- Initial value of resistance(R0) Change in resistance(Rt – R0) Change in temperature(Δt)

Q4) Explain the effect of temperature on resistance of 1) Metal Conductors 2) Insulators 3) Alloys. (6 marks)[Dec-15]Ans: Effect Of Temperature On ResistanceResistance of the material changes with the temperature. For different types of materials the amount of change in resistance due to change in temperature is different.

1. Pure Metals :- The resistance R is a temperature dependent quantity. For different types of

conductors(pure metals), the amount of change in resistance due to change in temperature will have different value.

Fig :For Pure Metals At low temperature, the charged particles acquire energy & starts oscillating about

their mean position. These vibrations cause obstruction to the flow of electrons or collide with the

electrons. Hence the resistance R increases with increase in temperature. Pure metals have positive temperature coefficient of resistance.

2. Alloy: Pure metals are rarely used. Instead metals alloy (E.g. Eureka maganin, etc.) are

used due to some of their advantage over the metals. The resistance of almost all the alloys increases with increase in temperature but

the rate of change in a resistance with temperature is less than that of metals. For some special alloys such as Manganin(formed from copper, manganese &

nickel) or Eureka(obtained from nickel & copper) the change in resistance with temperature is almost zero.

Alloys have positive temperature coefficient of resistance and some special alloys have almost zero RTC.

For alloys resistance remains almost constant with increase in temperature.

3. Insulators :- In case of insulators, resistance of material decreases with increase in

temperature. As temperature increases, some electrons acquire energy and become free for

conduction Due to this conductivity increases. Hence the material that acts as perfect insulators at low temperature may start

conducting at high temperature. Insulators have negative temperature coefficient of resistance.

Fig: Graph showing Effect of Temperature on Resistance