Doubt

Asked by arushidabhade | 9th Jul, 2020, 09:28: AM

Expert Answer:

In the arrangement shown, find current flowing through AB
 
Resistors 2R and R are connected in parallel in RHS of circuit. 
Let I be the current flowing through the circuit. 
L e t space I subscript 1 space b e space t h e space c u r r e n t space f l o w i n g space t h r o u g h space 2 R space a n d space I subscript 2 space b e space c u r r e n t space f l o w i n g space t h r o u g h space R space left parenthesis i. e. space A B space w i r e right parenthesis space
C u r r e n t space f l o w i n g space t h r o u g h space p a r a l l e l space c o m b i n a t i o n space a r e space n o t space s a m e. space
E f f e c t i v e space r e s i s tan c e colon space minus space
1 over R subscript p space equals space fraction numerator 1 over denominator 2 R end fraction plus space 1 over R space equals space fraction numerator 3 over denominator 2 R end fraction
E f f e c t i v e space r e s i s tan c e space equals space R plus fraction numerator 2 R over denominator 3 end fraction space equals space fraction numerator 5 R over denominator 3 end fraction space... space left parenthesis 1 right parenthesis
T h u s comma space c u r r e n t space f l o w i n g space i n space c i r c u i t space i s
space I space equals space V over R space equals space fraction numerator V over denominator begin display style bevelled fraction numerator 5 R over denominator 3 end fraction end style end fraction space equals space fraction numerator 3 V over denominator 5 R end fraction space... space left parenthesis 2 right parenthesis

I subscript 1 space equals space fraction numerator V subscript 2 over denominator 2 R end fraction space... space left parenthesis 3 right parenthesis
I subscript 2 space equals space V subscript 2 over R space... space left parenthesis 4 right parenthesis
I space equals space I subscript 1 space plus space I subscript 2 space
I space equals space space fraction numerator V subscript 2 over denominator 2 R end fraction space plus space V subscript 2 over R space equals V subscript 2 space open parentheses fraction numerator 3 over denominator 2 R end fraction close parentheses
T h u s comma space
V o l t a g e space a c r o s s space A B space i s comma space V subscript 2 space equals space fraction numerator 2 I R over denominator 3 end fraction
T h u s comma space f r o m space left parenthesis 4 right parenthesis comma space
c u r r e n t space f l o w i n g space t h r o u g h space A B space i s space
I subscript 2 space equals space fraction numerator fraction numerator 2 I R over denominator 3 end fraction over denominator R end fraction space equals space fraction numerator 2 I R over denominator 3 R end fraction space equals fraction numerator 2 space over denominator 3 end fraction open parentheses I close parentheses space
A l s o space f r o m space e q u a t i o n space left parenthesis 2 right parenthesis space
I subscript 2 equals space fraction numerator 2 space over denominator 3 end fraction open parentheses fraction numerator 3 V over denominator 5 R end fraction close parentheses space equals space fraction numerator 2 V over denominator 5 R end fraction space
 

Answered by Shiwani Sawant | 10th Jul, 2020, 12:20: AM