Question

in mesh analysis,first we have to assume independent mesh currents and apply KVL..what to do if there is an independent current source?

Answer 1

If there's an independent current source, it'll give you some extra information that you can use. For example, if you have a current source that supplies 3 A, you could know that \[i_3 = 3 A\] or that \[i_4-i_1 = 3A\] depending on your circuit.

Answer 2

but i have to multiply current by resistance to form kvl eqns...so what to do if there is no resistance?

Answer 3

Take this simple example: While I've drawn two loop currents, only one of them is unknown. We already know that \[i_2 = I_S\]

So if we apply KVL, we get the following equation:
\[R_1 \cdot i_1 + R_2 \cdot (-i_1+i_2) = 0 \]
Filling in what we already know, you'll get:
\[ R_1 \cdot i_1 + R_2 \cdot (-i_1+I_S) = i_1 \cdot (R_1 - R_2) + R_2 \cdot I_S = 0\]
One equation, with one unknown, so it's solvable.