A fixed resistor R1 = 5 Ω is connected in series with a parallel combination consisting of a fixed resistor R2 = 10 Ω and a variable resistor X (whose resistance can be adjusted from 0 Ω to 20 Ω).
The two free ends of the whole circuit serve as terminals S and T.
Respond to the following parts:
a. (i) Derive an expression for the equivalent resistance R_eq between S and T as a function of X.
b. (ii) For what value of X will the equivalent resistance become exactly 8 Ω? Show all algebraic steps.
c. (iii) For the value of X obtained in part (ii), determine the fraction of the total current that flows through resistor R2.