The circuit in Figure is a slide-type Wheatstone bridge.?It is used for determining an unknown resistance R_x in terms of the known resistances R₁, R₂, and R₀. The resistances R₁ and R₂ comprise a wire 1 m long. Point a?is a sliding contact that is moved along the wire to vary these resistances. Resistance R₁ is proportional to the distance from the left end of the wire (labeled 0 cm) to point a, and R₂ is proportional to the distance from point a to the right end of the wire (labeled 100 cm). The sum of R₁ and R_2?remains constant. When points a and b?are at the same potential, there is no current in the galvanometer and the bridge is said to be balanced. (Since the galvanometer is used to detect the absence of a current, it is called a null detector.) If the fixed resistance R₀ = 200 ?, find the unknown resistance R_x if

(a) The bridge balances at the 18-cm mark,

(b) The bridge balances at the 60-cm mark, and

(c) The bridge balances at the 95-cm mark.

Transcribed Image Text:

O cm R2 100 cm R1 ww R, Ro