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is made of uniform material and cross-se...

is made of uniform material and cross-sectional area, and it has uniform resistance per unit length. The potential gradient depends upon the current in the wire.
A potentiometer with a cell of emf `2 V` and internal resistance `0.4 Omega` is used across the wire `AB`. A standard cadmium cell of emf `1.02 V` gives a balance point at `66 cm` length of wire. The standard cell is then replaced by a cell of unknows emf `e` (internal resistance `r`), and the balance. Point found similarly turns out to be `88 cm` length of the wire. The length of potentiometer wire `AB` is `1 m`.
The reading of the potentiometer, if a `4V` battery is used instead of `e` is

A

`88.3 cm`

B

`47.3 cm`

C

`95 cm`

D

cannot be calculated

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will follow the given information and apply the principles of a potentiometer. ### Step 1: Understand the given data - EMF of the standard cadmium cell, \( E_1 = 1.02 \, V \) - Balance length for the standard cell, \( L_1 = 66 \, cm = 0.66 \, m \) - Balance length for the unknown EMF cell, \( L_2 = 88 \, cm = 0.88 \, m \) - Total length of the potentiometer wire, \( L = 1 \, m \) - EMF of the potentiometer cell, \( E = 2 \, V \) - Internal resistance of the potentiometer cell, \( r = 0.4 \, \Omega \) ### Step 2: Calculate the unknown EMF \( E_2 \) Using the formula for the balance condition of a potentiometer: \[ \frac{E_2}{E_1} = \frac{L_2}{L_1} \] Substituting the known values: \[ E_2 = E_1 \cdot \frac{L_2}{L_1} = 1.02 \cdot \frac{0.88}{0.66} \] Calculating \( E_2 \): \[ E_2 = 1.02 \cdot 1.3333 \approx 1.36 \, V \] ### Step 3: Find the balancing length when using a 4V battery Now, we need to find the new balance length \( L_2' \) when the unknown EMF cell is replaced by a 4V battery: Using the same formula: \[ L_2' = \frac{E_2}{E_1} \cdot L_1 \] Substituting the values: \[ L_2' = \frac{4}{1.02} \cdot 0.66 \] Calculating \( L_2' \): \[ L_2' = 3.9216 \cdot 0.66 \approx 2.586 \, m \] ### Step 4: Analyze the result Since the total length of the potentiometer wire is only 1 meter, a balance point cannot be achieved with a 4V battery because the calculated length exceeds the available length of the wire. ### Conclusion The reading of the potentiometer when using a 4V battery cannot be obtained as it exceeds the length of the potentiometer wire.
To solve the problem step by step, we will follow the given information and apply the principles of a potentiometer. ### Step 1: Understand the given data - EMF of the standard cadmium cell, \( E_1 = 1.02 \, V \) - Balance length for the standard cell, \( L_1 = 66 \, cm = 0.66 \, m \) - Balance length for the unknown EMF cell, \( L_2 = 88 \, cm = 0.88 \, m \) - Total length of the potentiometer wire, \( L = 1 \, m \) - EMF of the potentiometer cell, \( E = 2 \, V \) ...
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