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 $400mm$ and $588mm$ when $X$ is connected to $Y$ and $Z$, respectively. The length of the slide wire is $1.00m$. 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 $R=47\Omega$