(Solved) A Uniformly loaded DC distributor is fed at both ends with equal voltages. The voltage drop at the midpoint is...that of the DC distributor fed at one end.

Question : [GSECL JE] 

A Uniformly loaded DC distributor is fed at both ends with equal voltages, The voltage drop at the midpoint is...... that of the DC distributor fed at one end.

એકસમાન રૂપે ભારિત કરવામાં આવેલા DC વિતરકને બંને છેડેથી સમાન વૉલ્ટેજ પૂરો પાડવામાં આવે છે. મધ્યબિંદુ પરનો વોલ્ટેજ ઘટાડો એક છેડે પૂરા પાડવામાં આવેલા DC વિતરકથી...................છે.

A. Twice 

B. One-forth

C. One - half

D. One - third

Answer :

For distributor fed at one end :

Voltage drop for uniformly loaded distributor fed at one end = iR(lx - (x²/2)

(Derivation of above equation is given in DC distribution chapter of V. K. Mehta book) 

For voltage drop at mid point x = l/2

Substituting x = l/2

Voltage drop at mid point = 3iRl²/8...........................(1)

For distributor fed at both ends :

Voltage drop for uniformly loaded distributor fed at both ends with equal voltages = iR(lx - x²)/2

For voltage drop at mid point x = l/2

Substituting x = l/2

Voltage drop at mid point = iRl²/8.............................(2)

Comparing equation (1) and (2), 

A Uniformly loaded DC distributor is fed at both ends with equal voltages. The voltage drop at the midpoint is...one third... that of the DC distributor fed at one end.

Option (d) is correct. 

In provisional answer key of GSECL correct answer given is one fourth. But as per derivation correct answer is one third. 

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