1. 1. State the principle on which a potentiometer works. How can… - Vidyadip

Question

State the principle on which a potentiometer works. How can a given potentiometer be made more sensitive?
In the graph shown below for two potentiometers, state with reason which of the two potentiometers$, A$ or $B,$ is more sensitive.

Two metallic wires$, P_1$ and $P_2$ of the same material and same length but different cross$-$sectional areas$, A_1$ and $A_2$ are joined together and connected to a source of emf. Find the ratio of the drift velocities of free electrons in the two wires when they are connected $(i)$ in series, and $(ii)$ in parallel.

✓

Answer

The potential difference across any length of wire is directly proportional to the length provided current and area of cross section are constant i.e.$, ? ? = ??$ where $?$ is the potential drop per unit length.

It can be made more sensitive by decreasing current in the main circuit/decreasing potential gradient/increasing resistance put in series with the potentiometer wire.

Potentiometer $B$

Has smaller value of $\text{ }^V/_l\ ($slope/potential gradient$).$

In series, the current remains the same.

$I=neA_1V_{d1}=neA_2V_{d2}$
$\therefore\frac{V_{d1}}{V_{d2}}=\frac{A_2}{A_1}$
In parallel potential difference is same but currents are different.
$V=I_1R_1=neA_1V_{d1}\frac{\rho l}{A_1}=ne\rho V_{d1}l$
Similarly, $V=I_2R_2=ne\rho V_{d2}l$
$I_1R_1=I_2R_2$
$\therefore\frac{V_{d1}}{V_{d2}}=1$

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