In a potentiometer wire experiment the emf of a battery in the primary circuit is `20V` and its internal resistance is `5Omega`. There is a resistance box in series with the battery and the potentiometer wire, whose resistance can be varied from `120Omega` to `170Omega`. Resistance of the potentiometer wire is `75Omega`. The following potential differences can be measured using this potentiometer.

Options

A. A) 5V
B. B) 6V
C. C) 7V
D. D) 8V

Answer

To solve the problem step by step, we will calculate the potential difference that can be measured using the potentiometer based on the given values.

### Step 1: Identify the given values
- EMF of the battery (E) = 20 V
- Internal resistance of the battery (r) = 5 Ω
- Resistance of the potentiometer wire (R1) = 75 Ω
- Resistance of the resistance box (R) varies from 120 Ω to 170 Ω

### Step 2: Calculate the total resistance in the circuit
The total resistance (R_total) in the circuit when the resistance box is set to its minimum value (120 Ω) is:
\[ R_{\text{total}} = r + R + R1 \]
Substituting the values:
\[ R_{\text{total}} = 5 \, \Omega + 120 \, \Omega + 75 \, \Omega = 200 \, \Omega \]

### Step 3: Calculate the current when R = 120 Ω
Using Ohm's law, the current (I) in the circuit can be calculated as:
\[ I = \frac{E}{R_{\text{total}}} \]
Substituting the values:
\[ I = \frac{20 \, V}{200 \, \Omega} = 0.1 \, A \]

### Step 4: Calculate the potential difference across the potentiometer wire when R = 120 Ω
The potential difference (V) across the potentiometer wire can be calculated using:
\[ V = I \times R1 \]
Substituting the values:
\[ V = 0.1 \, A \times 75 \, \Omega = 7.5 \, V \]

### Step 5: Calculate the total resistance in the circuit when R = 170 Ω
Now, calculate the total resistance when the resistance box is set to its maximum value (170 Ω):
\[ R_{\text{total}} = r + R + R1 \]
Substituting the values:
\[ R_{\text{total}} = 5 \, \Omega + 170 \, \Omega + 75 \, \Omega = 250 \, \Omega \]

### Step 6: Calculate the current when R = 170 Ω
Using Ohm's law again:
\[ I = \frac{E}{R_{\text{total}}} \]
Substituting the values:
\[ I = \frac{20 \, V}{250 \, \Omega} = 0.08 \, A \]

### Step 7: Calculate the potential difference across the potentiometer wire when R = 170 Ω
Using the same formula for potential difference:
\[ V = I \times R1 \]
Substituting the values:
\[ V = 0.08 \, A \times 75 \, \Omega = 6 \, V \]

### Final Result
The potential differences that can be measured using the potentiometer range from 6 V (when R = 170 Ω) to 7.5 V (when R = 120 Ω). Therefore, the potential differences that can be measured are between 6 V and 7.5 V.