A potentiometer having the potential gradient of `2 mV//cm` is used to measure the difference of potential across a resistance of `10 ohm`. If a length of `50 cm` of the potentiometer wire is required to get null point, the current passing through the `10 ohm` resistor is (in `mA`)

Options

A. 1
B. 2
C. 5
D. 10

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Understand the given data
- Potential gradient (V/L) = 2 mV/cm
- Length of potentiometer wire (L) = 50 cm
- Resistance (R) = 10 ohms

### Step 2: Calculate the potential drop across the resistor
The potential drop (V) across the resistor can be calculated using the formula:
\[ V = \text{Potential Gradient} \times \text{Length} \]

Substituting the values:
\[ V = 2 \, \text{mV/cm} \times 50 \, \text{cm} \]
\[ V = 100 \, \text{mV} \]

### Step 3: Convert potential drop to volts
Since 1 mV = \(10^{-3}\) V, we convert 100 mV to volts:
\[ V = 100 \, \text{mV} = 100 \times 10^{-3} \, \text{V} = 0.1 \, \text{V} \]

### Step 4: Calculate the current through the resistor
Using Ohm's Law, the current (I) through the resistor can be calculated as:
\[ I = \frac{V}{R} \]

Substituting the values:
\[ I = \frac{0.1 \, \text{V}}{10 \, \Omega} \]
\[ I = 0.01 \, \text{A} \]

### Step 5: Convert current to milliampere
Since 1 A = 1000 mA, we convert the current to milliampere:
\[ I = 0.01 \, \text{A} = 0.01 \times 1000 \, \text{mA} = 10 \, \text{mA} \]

### Final Answer
The current passing through the 10 ohm resistor is **10 mA**.

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