W i t h space t w o space r e s i s tan c e space w i r e s space i n space t h e space t w o space g a p s space o f space space a space m e t r e space space b r i d g e space comma space t h e space b a l a n c e space p o i n t space space w a s space f o u n d space t o space b e space 1 divided by 3 space m space f r o m space t h e space z e r o space e n d . w h e n space a space 6 capital omega space c o i l space i s space c o n n e c t e d space i n space s e r i e s space w i t h space t h e space s m a l l e r space o f space t h e space t w o space r e s i s tan c e s space comma space t h e space b a l a n c e d space p o i n t space i s space s h i f t e d space t o space 2 divided by 3 space m f r o m space t h e space s a m e space e n d space. space f i n d space t h e space r e s i s tan c e space o f space t h e space t w o space w i r e s space.

Asked by yash.bisht9910 | 5th Jun, 2015, 02:07: PM

Expert Answer:

begin mathsize 12px style Let space straight R subscript 1 space and space straight R subscript 2 space be space the space two space resistances space of space the space wires space in space the space two space gaps. Since space the space balance space point space found space to space be space 1 divided by 3 space straight m space from space zero space end hence comma space straight l subscript 1 equals straight l equals 1 divided by 3 space straight m space and space straight l subscript 2 equals 100 minus straight l equals 1 minus 1 divided by 3 equals 2 divided by 3 From space the space principle space of space Wheatstone apostrophe straight s space bridge comma straight P over straight Q equals straight R over straight S rightwards double arrow space straight R subscript 1 over straight R subscript 2 equals fraction numerator straight l over denominator 100 minus straight l end fraction equals fraction numerator 1 divided by 3 over denominator 2 divided by 3 end fraction equals 1 half rightwards double arrow straight R subscript 2 equals 2 straight R subscript 1 Which space shows space that space straight R subscript 1 space less than space straight R subscript 2 When space 6 space straight capital omega space coil space is space connected space inseries space with space the space smaller space of space theresistance comma space the space point space is space shifted space to space 2 divided by 3 space from space the space same space end. Hence comma space straight l apostrophe equals 2 over 3 straight m and space left parenthesis 100 minus straight l apostrophe right parenthesis equals 1 minus 2 divided by 3 space equals space 1 divided by 3 space straight m From space the space principle space of space Wheatstone apostrophe straight s space bridge comma fraction numerator straight R apostrophe subscript 1 over denominator straight R apostrophe subscript 2 end fraction equals fraction numerator straight R subscript 1 plus 6 over denominator straight R subscript 2 end fraction equals fraction numerator straight l apostrophe over denominator 100 minus straight l apostrophe end fraction equals fraction numerator 2 divided by 3 over denominator 1 divided by 3 end fraction equals  fraction numerator straight R subscript 1 plus 6 over denominator 2 straight R subscript 1 end fraction equals fraction numerator 2 divided by 3 over denominator 1 divided by 3 end fraction equals 2 rightwards double arrow straight R subscript 1 equals 2 space straight capital omega Also comma space straight R subscript 2 equals 2 cross times 2 equals 4 straight capital omega end style

Answered by Priyanka Kumbhar | 5th Jun, 2015, 03:14: PM