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Q 36 of hc verma
find the potential diference Va-Vb in the circuits
ans 1)(E1/R1+E2/R2)/1/R1+1/R2+1/R2

ANS20same as above.
please answer its urgent.

madman

i am assuming E1 to be greater than E2
let the current in the upper arm of AB be I1 , I2 be the current in the lower arm and I be the current in AB
Vb-Va = IR2 = I1R1- E1= - E2 - I2R3
I1 = I + I2
multiplying by R2 we have
R2 I1 = R2 I + R2 I2
R2 I=R2 I1 - R2 I2
and
-E1 + I1 R1 + I R2 =0 } - 1 from loop rule
-E2 - I2 R3 +I R2 = 0 } - 2

substituting the value of I R2 in the first equation we have
-E1 + I1R1 + R2 I1 - R2 I2 = 0
&
subtracting the first and second equations we have
(E2 - E1) + I1 R1 + I2 R3
from the above two equations determine I1

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