In the given diagram #E_1# and #E_2# are the emfs of cells, #r_1# and#r_2# are the internal resistances of cells. #R# is the external resistance. What are the values of #I_1# and #I_2#?

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Answer 1 · 2017-08-13T17:10:21

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Applying Kirchhoff's voltage law in the loop containing #E_1,r_1 and R# we get

#R(I_1+I_2)+r_1I_1-E_1=0#

#=>12(I_1+I_2)+0.5*I_1-6=0#

#=>24I_1+24I_2+I_1-12=0#

#=>25I_1+24I_2=12.... [1]#

Applying Kirchhoff's voltage law in the loop containing #E_2,r_2 and R# we get

#R(I_1+I_2)+r_2I_1-E_2=0#

#=>12(I_1+I_2)+1*I_2-10=0#

#=>12I_1+12I_2+I_2-10=0#

#=>12I_1+13I_2=10.... [2]#

Multiplying [1] by 12 and [2] by 25 we get

#300I_1+288I_2=144...[3]#

#300I_1+325I_2=250.... [4]#

Subtracting [3] from [4] we get

#37I_2=106#

#=>I_2=106/37A~~2.86A#

Inserting #I_2=106/37# in [2]

#=>12I_1+13*106/37=10#

#I_1=(370-13*106)/(37*12)A~~-2.27A#