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In the circuit shown in figure below, E1...

In the circuit shown in figure below, `E_1` and `E_2` are two cells having emfs 2 V and 3 V respectively, and negligible internal resistances. Applying Kirchhoff.s laws of electrical networks, find the values of currents `I_1` and `I_2`.
 

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Consider the direction of currents as shown in the figure above.
By applying Kirchhoff.s second law in mesh (1), we get
`R_3(I_1  + I_2) + R_1I_1 - E_1 = 0`
`2(I_1 + I_2) + 1 xxI_1 = 2`
`implies 3I_ + 2I_2 = 2 " " ...(1)`
By applying Kirhchoff.s second law in mesh (2), we get ,
`R_3 (I_1 + I_2) + R_2I_2 - E_2 = 0`
`2(I_1 + I_2) + 6I_2 = 3`
`implies 2I_1 + 8I_2 = 3 " " ...(2)`
On solving equations( 1) and (2) , we get
`I_1 = 1/2 A and I_2 = 1/4 A`.
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