Question

A potentiometer is used for the comparison of e.m.f. of two cells {{E}_{1}}
and {{E}_{2}}
. For cell {{E}_{1}}
the no deflection point is obtained at 20cm
and for {{E}_{2}}
the no deflection point is obtained at 30cm
. The ratio of their e.m.f.'s will be [MP PET 1984]
A) 2/3 B) 1/2 C) 1 D) 2

Answer 1

Hii friend,

The comparison of end of two cents using potentiometer can be calculated by using the formula,

E =IRL
where,
E=> emf of the cell

I => current
R = resistance
l => length at which it shows the zero deflection.

Given,

E1 => I R (20).................(1)

E2 => I R (30)...........(2)

Dividing (1) and (2) ,

E1/E2 => 20/30

E1/E2 => 2/3

:- The radio of their emf is 2/3

Answer is option (A)..

Hope this helps you a little!!!

Answer 2

$\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}$

Potentiometer is a device that is used to measure electromotive force of cells.

If potentiometer can be used to calculate e.m.f of one cell then we can also find ratio of e.m.f of two cells.

Emf Or Electro motive force of a cell is the work done by cell in moving a unit charge to the conductor. It is also the product of resistance , current and the length of deflection shown by potentiometer. It is defined by the expression :

$\bigstar \: \orange{\mid{\underline{\overline{\textbf{e = irl}}}\mid}}$

In this equation :

• E = Electro Motive Force
• i= current
• r = resistance
• l = length of deflection shown by potentiometer.

$\blue{\mid{\underline{\overline{\textbf{Coming to question :-}}}\mid}}$

Now, after inputting the values we get Emf of first cell to be :

$\mapsto \: e_1 = i\times r\times 20 = 20ir$

Similarly, the Emf of second cell will be :

$\mapsto \: e_2 = i \times r \times 30 = 30ir$

Now ratio of Emf's of both the cells is :

$\mapsto \: \frac{e_1}{e_2} \\ \\\mapsto \frac{2 \times 10 \times ir}{3 \times 10 \times ir}$

$\mapsto \: \frac{2}{3} \times \cancel \frac{10}{10} \times \cancel \frac{ir}{ir}$

$\mapsto \: = \frac{2}{3}$

Thus the ratio of their Emf's is 2:3 .

Therefore Option A is correct.

______________________________________

BY SCIVIBHANSHU

THANK YOU

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