Calculate the resistance of a 2 m long nichrome wire of radius 0.321 mm. Resistivity of nichrome is `15xx10^(-6) Omega` m. If a potential difference of 10 V is applied across this wire, what will be the current in the wire ?

Answer

To solve the problem, we will calculate the resistance of the nichrome wire using the formula for resistance and then use Ohm's law to find the current flowing through the wire when a potential difference is applied.

### Step 1: Calculate the cross-sectional area (A) of the wire
The radius of the wire is given as \( r = 0.321 \, \text{mm} \). We need to convert this to meters:
\[ r = 0.321 \, \text{mm} = 0.321 \times 10^{-3} \, \text{m} = 3.21 \times 10^{-4} \, \text{m} \]
The cross-sectional area \( A \) of the wire can be calculated using the formula for the area of a circle:
\[ A = \pi r^2 \]
Substituting the value of \( r \):
\[ A = \pi (3.21 \times 10^{-4})^2 \approx 3.24 \times 10^{-7} \, \text{m}^2 \]

### Step 2: Calculate the resistance (R) of the wire
The resistance \( R \) of the wire can be calculated using the formula:
\[ R = \frac{\rho L}{A} \]
Where:
- \( \rho = 15 \times 10^{-6} \, \Omega \, \text{m} \) (resistivity of nichrome)
- \( L = 2 \, \text{m} \) (length of the wire)

Substituting the values:
\[ R = \frac{15 \times 10^{-6} \times 2}{3.24 \times 10^{-7}} \approx 92.6 \, \Omega \]

### Step 3: Calculate the current (I) using Ohm's Law
Ohm's Law states that:
\[ I = \frac{V}{R} \]
Where:
- \( V = 10 \, \text{V} \) (potential difference)

Substituting the values:
\[ I = \frac{10}{92.6} \approx 0.108 \, \text{A} \text{ or } 108 \, \text{mA} \]

### Final Answer
The current flowing through the wire when a potential difference of 10 V is applied is approximately \( 0.108 \, \text{A} \) or \( 108 \, \text{mA} \).

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