If the resistor or impedance is being connected in parallel to supernode, then what current value will be across that resistor or impedance?
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Generally we define a supernode around two nodes connected by a voltage source, in order to facilitate a solution to a circuit by the modified nodal analysis.
If you connect a resistor across a voltage source, you get a current through it determined by Ohm's Law, regardless of whether we're analyzing the circuit with MNA, mesh analysis, or any other method.
If a resistor is connected across the terminals of a supernode, then the resistor terminals will remain at the voltage across the terminals of the supernode. The resistor will allow current to flow between the terminals of the supernode. The current is dependent on the value of the resistor. The current can be calculated using Ohm's Law: I = V/R