In a potentiometer arrangement, a cell gives a balancing point at 75 cm length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emfs of two cells respectively is 3 : 2, the difference in the balancing length of the potentiometer wire in above two cases will be _____ cm.(In Integers)Correct answer is '25'. Can you explain this answer?

Question

Answer

At the balancing point, we know that emf is proportional to the balancing length, i.e. emf ∝ balancing length.
Now, let the emfs be 3ε and 2ε.
⇒3ε = k(75) _____ (1) and 2ε = k(l) _____ (2)
⇒ l = 50 cm
⇒ Difference = (75 - 50) cm = 25 cm

Answer

Given:
- The balancing point of the potentiometer wire with the first cell is 75 cm.
- The ratio of the emfs of the two cells is 3:2.

To find:
- The difference in the balancing length of the potentiometer wire when the cell is replaced by another cell of unknown emf.

Solution:
The balancing length of the potentiometer wire is given by the formula:

L = (E₁ / E₂) × d

Where:
- L is the balancing length of the wire
- E₁ is the emf of the first cell
- E₂ is the emf of the second cell
- d is the total length of the potentiometer wire

We are given that the balancing length with the first cell is 75 cm.

Step 1:
Let's assume the total length of the potentiometer wire is d.

Step 2:
Using the formula, we can write the equation for the balancing length with the first cell:

75 = (E₁ / E₂) × d

Step 3:
Since the ratio of the emfs of the two cells is 3:2, we can write:

E₁ / E₂ = 3/2

Step 4:
Substituting the value of (E₁ / E₂) from Step 3 into the equation from Step 2:

75 = (3/2) × d

Step 5:
Simplifying the equation, we get:

d = (75 × 2) / 3
d = 50 cm

So, the total length of the potentiometer wire is 50 cm.

Step 6:
Now, let's calculate the balancing length with the second cell using the formula:

L = (E₁ / E₂) × d

Substituting the given values:

L₂ = (3/2) × 50
L₂ = 75 cm

Step 7:
The difference in the balancing lengths is given by:

Difference = L₂ - L₁
Difference = 75 - 75
Difference = 0 cm

Therefore, the difference in the balancing length of the potentiometer wire when the cell is replaced by another cell of unknown emf is 0 cm.

Answer

At the balancing point, we know that emf is proportional to the balancing length, i.e. emf ∝ balancing length.
Now, let the emfs be 3ε and 2ε.
⇒3ε = k(75) _____ (1) and 2ε = k(l) _____ (2)
⇒ l = 50 cm
⇒ Difference = (75 - 50) cm = 25 cm

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