Question

Figure shows a circuit that may be used to compare the resistance $R$ of an unknown resistor with a $100 \, \Omega$ standard. The distances $l$ 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 $R$ ?

• A. $32\, \Omega$
• B. $47\, \Omega$
• C. $68 \, \Omega$
• D. $147 \, \Omega$

Answer 1

Answer: (B)

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 is proportional to the potential difference across the $100 \Omega$ resistor and resistor $R$.
$\frac{100+R}{100}=\frac{588}{400}$
or $ R=47 \,\Omega$