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CBSE Class 10 Answered

two wires of same material has length in ratio 1:2. If the difference in their series and parallel equivalent is 21 ohm then calculate the resistances of the wire.
Asked by Aritra | 16 Apr, 2019, 11:43: PM
answered-by-expert Expert Answer
A s space w e space k n o w space r e s i s tan c e space o f space t h e space w i r e space i s space d i r e c t l y space p r o p o r t i o n a l space t o space l e n g t h space o f space t h e space w i r e space left parenthesis R space equals space rho l over A right parenthesis
sin c e space t h e space r a t i o space o f space l e n g t h space i s space 1 divided by 2
l e t s space a s s u m e space t h e space r e s i s tan v e space o f space t h e space f i r s t space w i r e space i s space R space t h e n space r e s i s tan c e space o f space t h e space s e c o n d space w i r e space w o u l d space b e space 2 R
s o space i f space t h e space r e s i s t o r space a r e space c o n n e c t e d space i n space s e r i e s
e q u i v a l e n t space r e s i s tan c e space R subscript s space space equals space R plus 2 R space equals space 3 R
i f space t h e space r e s i s t o r s space a r e space c o n n e c t e d space i n space p a r a l l e l
e q u i v a l e n t space r e s i s tan c e space R subscript p space equals space space fraction numerator R cross times 2 R over denominator R plus 2 R end fraction space equals space fraction numerator 2 R squared over denominator 3 R end fraction space equals space 2 over 3 R
a n d space i t s space g i v e n space R subscript s minus R subscript p space equals space 21 space o h m
s o space comma 3 R minus 2 over 3 R space equals space 21
fraction numerator 9 R space minus space 2 R over denominator 3 R end fraction space equals space 21
fraction numerator 7 R over denominator 3 R end fraction space equals space 21

s o l v i n g space t h i s space e q u a t i o n space w e space g e t space t h e space v a l u e space o f space R space equals space 9 space o h m
Answered by Ankit K | 17 Apr, 2019, 10:35: AM
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