In an experiment with a potentiometer, VB = 10V. R is adjusted to be 50 Ω. A student wanting to measure voltage E1 of a battery finds no null point possible. He then diminishes R to 10 Ω and is able to locate the null point on the last segment of the potentiometer. Find the resistance of the potentiometer wire and potential drop per unit length across the wire in the second case.
Equivalent resistance of the potentiometer = 50 Ohm + R’
Equivalent voltage across the potentiometer = 10 V
Current through the main circuit I = 10/(50 Ohms +R’)
Potential difference across wire of potentiometer is:
When 50 ohms resistors is used
2R’ < 400
R’ < 200 Ohms
When 10 Ohm resistor is used
160 < R’ < 200
When the resistor is between 160 Ohms and 200 Ohms,
The potential gradient is given as
k > 2 V/m
When the potential drop across 300 cm wire is < 8 V
k < 2 2/3 V/m