**Can we use mesh analysis and get current in 1ohm resistor....and is not then why? **
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Ask yourself what if we shorted out the 3 ohm resistor. Would 3 amp still flow? – Andy aka Sep 23 '20 at 07:23
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The answer is yes, you can. Just set it up in the normal way. You'll have two mesh currents and two equations. You'll know one of the mesh currents but you won't know the voltage across the current source. So it is still two unknowns, too. – jonk Sep 23 '20 at 07:32
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I'm assuming you know how to do mesh. If so, you really should have no problems. If you need help setting how to set it up, let me know. – jonk Sep 23 '20 at 08:58
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Assume counter-clockwise currents for the mesh, you find:$$\begin{align*}V_{I_1=3\:\text{A}}-R_{3\:\Omega}\cdot I_1-R_{1\:\Omega}\cdot \left(I_1-I_2\right)&=0\:\text{V}\\\\-R_{1\:\Omega}\cdot \left(I_2-I_1\right)-R_{2\:\Omega}\cdot I_2&=0\:\text{V}\end{align*}$$You know \$I_1\$. Just solve for \$I_2\$ and \$V_{I_1=3\:\text{A}}\$. – jonk Sep 23 '20 at 11:29