A fixed resistor R1 = 5 Ω is connected in series with a parallel combination…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits
Problem
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:
(i) Derive an expression for the equivalent resistance R_eq between S and T as a function of X.
(ii) For what value of X will the equivalent resistance become exactly 8 Ω? Show all algebraic steps.
(iii) For the value of X obtained in part (ii), determine the fraction of the total current that flows through resistor R2.