Answer

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**Hint:**In potentiometer we find the balancing length of the circuit. When the length of the wire is increased it directly displaces the length of the wire where the null point is observed before. We will suppose a length where the balance point observed and then find the length of the second balance point when the wire length increased and check whether the balancing length increased or not.

**Formula used:**

$\dfrac{E}{V}$ =$\dfrac{l}{L}$ where E is cell voltage, V is driving source, $l$ is balancing length and L is length of wire

**Complete step by step answer:**

Step 1:

Let the resistance of the wire be denoted by $R$ of length ${L_1}$, and the driving source be V.

We assume that before increasing the length of wire we have the balancing length at ${l_1}$ and a cell voltage = E

Step 2:

So, from the formula of balancing point we can write $\dfrac{E}{V}$ =$\dfrac{{{l_1}}}{{{L_1}}}$ ………………..….. (1)

Step 3:

After changing the length of the potentiometer wire, the new length is${L_2}$, and the new balancing length will be${l_2}$

Now, $\dfrac{E}{V}$ =$\dfrac{{{l_2}}}{{{L_2}}}$ …………..…… (2)

Step 4:

By equating both the equation (1) and (2)

We will get, ${l_2}$ =${l_1}$ $\dfrac{{{L_2}}}{{{L_1}}}$

Or we can write it as $\dfrac{{{l_1}}}{{{L_1}}} = \dfrac{{{l_2}}}{{{L_2}}}$ …………….... (3)

We know that ${L_2}$ >${L_1}$ and from the eqn(3) we can state that ${l_2}$ >${l_1}$

**This means by increasing the length of the wire the balancing length will also increase. Therefore, option A is the correct answer.**

**Additional information:**

Application of potentiometer:

- The potentiometer is used as a voltage divider in the electronic circuit and compares the emf of a battery cell with a standard cell.

- The potentiometer is used in radio and television receivers for volume control. Tone control and linearity control.

- The potentiometer is used in medical equipment.

- It is used in the wood processing machine.

- It is used in injection mold machines.

- A potentiometer is widely used as user controls and may control a very wide variety of equipment functions.

**Note:**

When two things are equal with each other and then one thing increases or decreases, the other thing automatically does the same thing. In equation 3 the right-hand side in the denominator is smaller than the left-hand side denominator then this rule will be followed in the numerator also and hence we reached our conclusion of increasing the length of balancing.

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