(26 Ω Ω )

Sol. Step 1: Apply Kirchhoff's Current Law (KCL)
At the junction where the current splits, the incoming current equals the sum of the outgoing currents. This is already verified by the given values.

Step 2: Determine the potential at the junction
Consider the loop containing the 100 V battery and the resistor. Assuming the other end of the 100 V battery is connected to ground , the voltage across the resistor is calculated using Ohm's Law:

The potential at the common junction (Node A) relative to the ground is the battery voltage plus the voltage drop across the resistor (depending on polarity, the common problem configuration suggests they add up):

Step 3: Apply Ohm's Law to the branch with R
The potential difference across the unknown resistor is the potential at the junction, (assuming the other side of is at the same potential as the 100 V source reference point in that specific problem configuration). The current flowing through is .

Step 4: Solve for R
Rearrange the equation to find the value of :