Figure `6.49` shows a circuit that may be used to compare the resistance `R` of an unknown resistor with a `100 Omega` standard. The distance `l` from one end of the potentiometer slider wire to the balance point are `400 mm` and `588 mm` when `X` is connected to `Y` and `Z`, respectively. The length of the slide wire is `1.00 m`. What is the value of resistance `R`?

Options

A. `32 Omega`
B. `47 Omega`
C. `68 Omega`
D. `147 Omega`

Answer

B

Explanation

When `X` is connected to `Y`, the balance length `l` is proportional to the potential difference across the `100 Omega` resistor. When `X` is connected to `Z`, the balance length length is proprtional to the potential difference across the `100 Omega` resistor and resistor `R`.
`(100 + R)/(100) = (588)/(400)` or `R = 47 Omega`