a circuit is set up as shown in the figure,calculate the current and p.d. across R1,R2 and R3 when (1)keys K1 and K2 both are closed (2) key K1 is closed K2 is open (3)key K1 is open and K2 is closed.

Asked by nisha_vini29 | 28th May, 2015, 10:23: PM

Expert Answer:

(1) When keys K1 and K2 both are closed,

 
 

begin mathsize 12px style In space this space case space circuit space is space closed. space Current space will space flow space through space the space all space resistances. straight R subscript 2 space and space straight R subscript 3 space are space parallel. space Hence comma space equivalent space resistance space will space be comma 1 over straight R subscript straight p equals 1 over straight R subscript 2 plus 1 over straight R subscript 3 straight R subscript straight p equals fraction numerator straight R subscript 2 cross times straight R subscript 3 over denominator straight R subscript 2 plus straight R subscript 3 end fraction equals fraction numerator 6 cross times 4 over denominator 6 plus 4 end fraction equals 24 over 10 equals 2.4 space straight capital omega equivalent space resistance space of space complete space circuit comma space straight R space equals space straight R subscript 1 plus straight R subscript straight p space equals space 6 plus 2.4 equals 8.4 space straight capital omega Total space current space of space the space circuit comma space straight I space equals space straight V over straight R equals fraction numerator 2.4 over denominator 8.4 end fraction equals 0.272 space straight A From space the space figure comma space current space throught space straight R subscript 1 space will space be space straight I comma space space straight i. straight e. space 0.272 straight A Potential space across space straight R subscript 1 space is space straight V subscript 1 equals straight I space straight R subscript 1 equals 0.272 cross times 6 equals 1.636 space straight V  Let space straight I subscript 2 comma space straight I subscript 3 space be space the space current space through space straight R subscript 2 space and space straight R subscript 3 space respectively. straight I subscript 2 space straight R subscript 2 equals straight I subscript 3 space straight R subscript 3 fraction numerator straight I subscript 2 space over denominator straight I subscript 3 end fraction equals straight R subscript 3 over straight R subscript 2 equals 4 over 6 equals 0.667 space straight I subscript 2 space equals 0.667 straight I subscript 3 and space straight I equals straight I subscript 2 plus straight I subscript 3 equals space 0.272 equals 0.667 straight I subscript 3 plus straight I subscript 3 space 0.272 equals 1.667 straight I subscript 3 straight I subscript 3 equals 0.163 straight A rightwards double arrow space straight I equals straight I subscript 2 plus 0.163 equals space 0.272 rightwards double arrow straight I subscript 2 equals 0.109 space straight A Hence comma space Current space through space straight I subscript 2 space is space 0.109 space straight A space and space through space straight I subscript 3 space is space 0.163 space straight A. Potential space across space straight R subscript 2 space is space straight V subscript 2 equals straight I subscript 2 straight R subscript 2 equals 0.109 cross times 6 equals 0.654 space straight V Since space straight R subscript 2 space and space straight R subscript 3 space are space parallel space potential space across space them space will space be space same. space Hence comma space potential space across space straight R subscript 3 space will space be space 0.654 space straight V left parenthesis 2 right parenthesis space When space straight K subscript 1 space is space closed space and space straight K subscript 2 space is space open comma space current space flow space through space straight R subscript 1 space and space straight R subscript 2 In space this space case space straight R subscript 1 space and space straight R subscript 2 space end subscript are space in space series equivalent space resistance space of space complete space circuit comma space straight R space equals space straight R subscript 1 plus straight R subscript 2 space equals space 6 plus 6 equals 12 space straight capital omega Current space through space the space circuit space is space straight I comma space equals space fraction numerator 4.2 over denominator 12 end fraction equals 0.35 space straight A Hence comma space current space through space straight R subscript 1 space and space straight R subscript 2 space is space 0.35 space straight A end style
 
begin mathsize 12px style Potential space across space straight R subscript 1 space is space straight V subscript 1 equals IR subscript 1 equals 0.35 cross times 6 equals 2.1 space straight V Potential space across space straight R subscript 2 space is space straight V subscript 2 equals IR subscript 2 equals 0.35 cross times 6 equals 2.1 space straight V end style
 
(3)  When keys K1 and K2 both are open,
In this case compelete circuit will remain open. hence no current through the circuit.
 

Answered by Priyanka Kumbhar | 29th May, 2015, 04:35: PM