The sliding contact C is at one fourth of the length of the potentiometer wire (AB) from A as shown in the circuit diagram. If the resistance of the wire AB is R0, then the potential drop (V) across the resistor R is [figure]
- 2V0 R2R0 + 3R
- 4V0 R3R0 + 16R
- 4V0 R3R0 + R
- 2V0 R4R0 + R
Answer
(2) 4V0 R3R0 + 16R
Solution
Resistance of AC = R04, resistance of CB = 3R04
R is connected between A and C, i.e. in parallel with AC:
Rp = R R04R + R04 = R R04R + R0
Rp is in series with CB across V0:
V = V0 RpRp + 3R04
= V0 R R04R + R0 R R04R + R0 + 3R04
= V0 4R4R + 3(4R + R0)
V = 4V0 R3R0 + 16R
Answer: (2)