In a potentiometer circuit when two cells of e.m.f. 1.5 volt and 1.2 volt are connected to assist each other, balancing length is 270 cm. What will be the balancing length in cm when these two cells a

Question

In a potentiometer circuit when two cells of e.m.f. 1.5 volt and 1.2 volt are connected to assist each other, balancing length is 270 cm. What will be the balancing length in cm when these two cells are connected in opposition?

TestHub · Accepted Answer

Let the potential gradient of the potentiometer wire be $k$ .

When the cells assist each other, the equivalent EMF is $E_{1} + E_{2}$ .

$E_{1} + E_{2} = k l_{1}$

$1.5 + 1.2 = k \times 270$

$2.7 = 270 k$

When the cells are connected in opposition, the equivalent EMF is $E_{1} - E_{2}$ .

$E_{1} - E_{2} = k l_{2}$

$1.5 - 1.2 = k l_{2}$

$0.3 = k l_{2}$

Dividing the two equations, we get:

$\frac{2.7}{0.3} = \frac{270}{l _{2}}$

$9 = \frac{270}{l _{2}}$

$l_{2} = 30$ cm

Answer: $30$

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