Can we use nodal analysis without any information about the current
Can we use nodal analysis with only the voltage of the source and resistances of components in the circuit?


Yes. In fact, you may also use it for Mesh Current Analysis as well, the choice is yours. However, one analysis might be easier than another analysis. As long as there is a source of any type at anywhere, you can solve for what you're looking for.

The way I described how to find the current at a node is:

\$i_{x}= (V_{1}-V_{2})/R_{between} \$

Where \$i_x\$ is an arbitrary variable for current at the node, \$V_{1}\$ is the voltage at the branch directly onto the node, \$V_2\$ is the voltage at the branch next to the resistor next to \$V_1\$ and \$R_{between}\$ is a resistor value between the nodes. If there is a voltage source at \$V_1\$ or \$V_2\$, then it will become a numerical value rather than a variable.

Consider the following example.







simulate this circuit &ndash; Schematic created using CircuitLab

Easy right? We'll just solve for one node as you can repeat the process.

\$ \displaystyle i_1=\frac{V_1-V_2}{R_1}=\frac{5-V_2}{100}\$

You can do the same with \$V_2\$ and \$V_3\$.

\$ \displaystyle i_2=\frac{V_2-V_3}{R_2}=\frac{V_2-V_3}{100}\$

You now have a system of equations to solve for \$V_2\$ and \$V_3\$. If you have a resistor between your node and ground, then treat your ground as a separate node with the voltage being zero instead.