Question

How to solve resistivity in numericals class 10?

Answer 1

To solve problems related to **resistivity** in Class 10, you need to understand the relationship between resistivity, resistance, and the material’s dimensions.

### Key Formula:
The resistivity \( \rho \) of a material is related to the resistance \( R \) of a conductor by the formula:

\[
R = \rho \times \frac{L}{A}
\]

Where:
- \( R \) = Resistance of the conductor (measured in ohms, \( \Omega \))
- \( \rho \) = Resistivity of the material (measured in ohm meters, \( \Omega \cdot m \))
- \( L \) = Length of the conductor (measured in meters, \( m \))
- \( A \) = Cross-sectional area of the conductor (measured in square meters, \( m^2 \))

### Solving Steps:
1. **Identify the given values**: Look for information such as the length \( L \), area \( A \), resistance \( R \), and resistivity \( \rho \) in the question.

2. **Rearrange the formula** to solve for the unknown:
   - If you're given the **resistivity** \( \rho \), use \( R = \rho \times \frac{L}{A} \) and solve for \( \rho \):
   \[
   \rho = R \times \frac{A}{L}
   \]
   - If you're solving for **resistance** \( R \), use the original formula \( R = \rho \times \frac{L}{A} \).

3. **Substitute the values**: Put the known values into the formula and perform the necessary calculations.

### Example Problem:

**Problem**: A wire has a resistance of 5 ohms. If the length of the wire is 2 meters and its cross-sectional area is \( 1 \times 10^{-6} \, m^2 \), calculate the resistivity of the material of the wire.

**Solution**:
- Given:
  - \( R = 5 \, \Omega \)
  - \( L = 2 \, m \)
  - \( A = 1 \times 10^{-6} \, m^2 \)

- Use the formula:
  \[
  \rho = R \times \frac{A}{L}
  \]

- Substitute the values:
  \[
  \rho = 5 \, \Omega \times \frac{1 \times 10^{-6} \, m^2}{2 \, m}
  \]

- Simplify:
  \[
  \rho = 5 \times \frac{1 \times 10^{-6}}{2} = 5 \times 0.5 \times 10^{-6} = 2.5 \times 10^{-6} \, \Omega \cdot m
  \]

So, the resistivity \( \rho \) of the material is \( 2.5 \times 10^{-6} \, \Omega \cdot m \).

### Tips:
- Always check the units to ensure they are consistent (length in meters, area in square meters).
- Resistivity is a property of the material, so it's usually constant for a given material at a specific temperature.
- If temperature changes, resistivity may also change, but for basic Class 10 problems, you can generally assume temperature is constant.

Let me know if you need more examples or help with specific questions!