Slightly Translated Parallel Electrical Circuit Analysis
The easiest way is to use the \$Y-\Delta\$ transformation:

Wikipedia



You find that

$$\begin{align}
R_1 &amp;= \frac{R_bR_c}{R_a+R_b+R_c} \\
R_2 &amp;= \frac{R_aR_c}{R_a+R_b+R_c} \\
R_3 &amp;= \frac{R_aR_b}{R_a+R_b+R_c}
\end{align}$$

Once you have transformed a triangle (either R1-R2-R3 or R3-R4-R5), you will find that you can simplify the equivalent resistance as usual.

For example, given that they're all \$100\Omega\$, \$R_1' = R_2' = R_3' = \frac{100^2}{300}\Omega = \frac{100}{3}\Omega\$. You can then work out the equivalent resistance

$$R_{eq} = \frac{100}{3}\Omega + \frac{1}{2}\left( 100 + \frac{100}{3}\right)\Omega = 100\Omega$$

In order to do the same with Nodal analysis, you want to calculate the current through the voltage source. The equivalent resistance is then the applied voltage divided by the current through the source. But if you really want to use nodal analysis on this circuit, you will have to resort to source shifting. By doing so, you can convert the voltage sources to their Northon equivalent, allowing you to use nodal analysis.







simulate this circuit &ndash; Schematic created using CircuitLab

You can apply Nodal analysis in the usual way and calculate the total current by summing the currents through R4 and R5.

Also consider looking up the Mesh current analysis, as this method doesn't require you to do source-shifting.

Another alternative, is by using Modified nodal analysis. You then add one unknown (the current through the voltage source \$i_V\$) and one equation (the applied voltage equation \$v_+ - v_- = 1V\$). You can then apply regular Nodal analysis, but using \$i_V\$ as an additional term in the other KCL equations. The added equation allows the system of equations to be solved.