Question
  1.  
  1. State the principle on which a potentiometer works. How can a given potentiometer be made more sensitive?
  2. In the graph shown below for two potentiometers, state with reason which of the two potentiometers, A or B, is more sensitive.
  1. Two metallic wires, P1 and P2 of the same material and same length but different cross-sectional areas, A1 and A2 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

  1.  
  1. 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., 𝐸 𝑙 = 𝜙𝑙 where 𝜙 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.

  1. Potentiometer B

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

  1. 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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