1.

In the given circuit values are as follows epsilon_(1)=2V, epsilon_(2)=4V, R_(1)=1Omega and R_(2)=R_(3)=1Omega. Calcualte the Currents through R_(1), R_(2) and R_(3).

Answer»

Solution :
LET `i_(1), i_(2)`are CURRENTS across `R_(1) and R_(3)`.
`(i_(1)+i_(2))` is current across `R_(2)`.
Their DIRECTION are taken as shown
From Kirchoff.s second LAW for AGFBA LOOP
`-i_(1)R_(1)-(i_(1)+i_(2))R_(2)+E_(1)=0`
`i_(1)+i_(1)+i_(2)=2 rArr 2i_(1)+i_(2)=2rarr(1)`
From Kirchooff.s second law for BCDEB loop
`-i_(2)R_(3)-(i_(1)+i_(2))R_(2)+E_(2)=0`
`i_(2)+i_(1)+i_(2)=rArr i_(2)+2i_(2)=4rarr(2)`
Solving equation (1) and (2)
we get `i_(1)=0A, i_(2)=2A`
Thus currents across `R_(1)` is 0,
while across `R_(3)` and R_(2)` are 2A each


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