Question

The linear slide wire AB in the circuit shown has a length of 100 cm. Where along its length should contact C be placed to provide exactly 8.00 V at $V_o$? The voltage of the Weston cell is 1.02 V.

Short answer

The contact C is placed at a distance $12.75\mathrm{cm}$from B towards A.

Step-by-step solution

Step 1. Given Information

Given a voltage follower circuit using an Op-Amp.

It also has a Weston cell connected in the feedback loop.

The output Voltage is 8 V.

The length of the slide wire is 100 cm.

We are asked to identify the location of the contact in the slide wire.

Step 2. Location of the contact in a slide wire and calculate its length for the circuit

The Op-Amp has a very high input impedance. So the voltage of the Weston cell will only appear at the resistance BC.

i.e.; $V_{BC}=1.02V$

Now, according to the voltage divider principle, we have;

$V_{BC}=\frac{BC}{AB}{V}_o$

Substituting the values of $V_{BC},V_{o}andAB$, we get;

$$\begin{gathered} 1.02V=\frac{BC}{100cm}\times 8V \\ \Rightarrow BC=\frac{102}{8}cm=12.75cm \end{gathered}$$

So, point C is at a distance of $12.75\mathrm{cm}$from B.