Current Electricity-17

When both switches are closed the 50-ohm resistor
gets short. With both switches open, we can apply KVL to find the current I in the 100ohm resistor. With the switches closed, the 100ohm resistor and R will be in parallel.The potential difference across them is the same and we can express the current i₁ in the 100 ohm in terms of the current I total flowing into the parallel branch whose resistance is R, and the resistance of the 100-ohm resistor. I depends on the equivalent resistance when both switch is closed, so we can express i₁ = I in terms of R and solve for R.