A 20 m long potentiometer wire has a resistance of 20 Ohm. It is connected in series with a battery of emf 3V and resistance of `10 Omega`. The internal resistance of cell is negligible. If the lenth can be read accurately up to 1 mm, the potentiometer can read voltage:

Options

A. A) up to maximum of 0.2 mV
B. B) with an accuracy of 0.2 mV
C. C) with an accuracy of 0.1 mV
D. D) upto maximum of 2V

Answer

To solve the problem step by step, we need to analyze the given information and apply the relevant formulas.

### Step 1: Understand the Circuit
We have a potentiometer wire of length 20 m and resistance 20 Ohm connected in series with a battery of EMF 3V and a resistance of 10 Ohm. The internal resistance of the cell is negligible.

### Step 2: Calculate Total Resistance
The total resistance in the circuit (R_total) is the sum of the resistance of the potentiometer wire and the external resistance:
\[ R_{\text{total}} = R_{\text{pot}} + R_{\text{ext}} = 20 \, \Omega + 10 \, \Omega = 30 \, \Omega \]

### Step 3: Calculate the Current (I)
Using Ohm's law, we can find the current flowing through the circuit:
\[ I = \frac{V}{R_{\text{total}}} = \frac{3 \, V}{30 \, \Omega} = 0.1 \, A \]

### Step 4: Calculate the Potential Gradient (k)
The potential gradient (k) across the potentiometer wire can be calculated as:
\[ k = \frac{V_{\text{pot}}}{L} \]
Where \( V_{\text{pot}} \) is the voltage across the potentiometer wire and \( L \) is the length of the wire.

The voltage across the potentiometer wire can be calculated as:
\[ V_{\text{pot}} = I \times R_{\text{pot}} = 0.1 \, A \times 20 \, \Omega = 2 \, V \]

Now, substituting the values:
\[ k = \frac{2 \, V}{20 \, m} = \frac{2 \, V}{20000 \, mm} = 0.0001 \, V/mm \]

### Step 5: Calculate the Maximum Voltage Reading
Since the potentiometer can read voltage accurately up to 1 mm, the maximum voltage that can be read (V_read) is:
\[ V_{\text{read}} = k \times \text{length} = 0.0001 \, V/mm \times 1 \, mm = 0.0001 \, V = 0.1 \, mV \]

### Step 6: Conclusion
Thus, the potentiometer can read a voltage of up to 0.1 mV.

### Summary of the Steps:
1. Calculate total resistance in the circuit.
2. Use Ohm's law to find the current.
3. Calculate the voltage across the potentiometer wire.
4. Determine the potential gradient.
5. Calculate the maximum voltage reading based on the length that can be read accurately.