The potentiometer wire 10m long and 20 ogm resistance is connected to a 3 volt emf battery and a 10ohm resistance. The value of potential gradient in volt/m of the wire will be

Options

A. 1
B. 0.2
C. 0.1
D. 0.02

Explanation

To find the potential gradient of the potentiometer wire, we can follow these steps:

### Step 1: Understand the Circuit
We have a potentiometer wire of length 10 m and resistance 20 ohms connected in series with a 10-ohm resistor and a 3-volt battery.

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

### Step 3: Calculate the Current in the Circuit
Using Ohm's Law, the current (I) in the circuit can be calculated as:
\[ I = \frac{V}{R_{\text{total}}} \]
Where V is the voltage of the battery (3 volts):
\[ I = \frac{3 \, \text{V}}{30 \, \Omega} = \frac{1}{10} \, \text{A} \]

### Step 4: Calculate the Potential Drop across the Potentiometer Wire
The potential drop (V_wire) across the potentiometer wire can be calculated using Ohm's Law:
\[ V_{\text{wire}} = I \times R_{\text{potentiometer}} \]
\[ V_{\text{wire}} = \left(\frac{1}{10} \, \text{A}\right) \times 20 \, \Omega = 2 \, \text{V} \]

### Step 5: Calculate the Potential Gradient
The potential gradient (k) is defined as the potential drop per unit length of the wire:
\[ k = \frac{V_{\text{wire}}}{L} \]
Where L is the length of the wire (10 m):
\[ k = \frac{2 \, \text{V}}{10 \, \text{m}} = 0.2 \, \text{V/m} \]

### Conclusion
The potential gradient of the potentiometer wire is \(0.2 \, \text{V/m}\).

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