Question

A 900 MW power station transmits power at a potential difference of 60, 000 V

a) Find the current.

b) Write down the equation for the resistance in terms of the resistivity.

c) If the power loss is 110 MW, over the length of the 200 km power line, find the resistivity of the line, if its cross section is 9 cm ².

d) Write down the equation for the magnetic field due to a long conductor.

e) Find the strength of the magnetic field for the current in part a, 20 m from the line.

f) You take a length of the line and wind it tightly, to form a solenoid of length L= 0.6 m. How many turns are in the solenoid?

g) What is the field inside the solenoid?

Answer 1

(a) Solution :

Given : Power = 900MW , Potential Difference = 60,000 V= 60 kW

We know,  Power(P) = Potential Difference Current = VI

I = P / V

= 900 X 10⁶ / 60 X 10³

= 15 X 10³ Ampere = 15 kilo-Ampere= 15 kA

(b) Solution : Resistance (R) of conducting materials depends upon following factors :

(i) Length (L) :Resistance of material is directly proportional to its length i.e. R L

(ii) Area of Cross-Section (A) : Resistance of material is inversely proportional to area of cross section i.e. R 1 / A

combining (i) and (ii) we get  

R L / A

R = L /A , Where (rho) is constant of proportionality known as Resistivity.It depends upon nature or material of conductor.

This is a equation of resistance (R) in terms of resistivity ().

(c) Solution : We know P=V X I

= ( I X R) X I ; (V = I X R (Ohm's Law))

= I² X R

P =  I²   L / A (Since, R = L /A)

from above,    = P A / I² L  

substituting given values in above formula with standard units,

= 110 X 10⁶ X 9 X10^-4 / (15X10³ )² X 200X10³

= 2.2 X10^-9 Ohm-meter = 2.2 X10^-9-m = 2.2 -nm

(d) Magnetic field due to straight infinite-long conductor, B =( 0 / 4 ) X (2 I / r)

  Where 0 = Magnetic Permeability = 4 X10-7 H/m

I = Current In the Conductor

r = distance of point (where we are calculating field) from conductor

(g) Solution : Magnetic field inside solenoid B = 0 n I

where n is no. of turns per unit length . n= N / L

and I is current flow in solenoid.