A rectangular carbon block has dimensions `1.0 cmxx 1.0 xx50 cm`.
(i) What is the resistance measured between the two square ends ?
(ii) Between two opposing rectangular faces ?
Resistivity of carbon at `20^(@)C" is "3.5xx10^(-5)Omegam`.

Answer

To solve the problem step by step, we will calculate the resistance of the rectangular carbon block for both scenarios: between the two square ends and between the two opposing rectangular faces.

### Given Data:
- Dimensions of the carbon block: \(1.0 \, \text{cm} \times 1.0 \, \text{cm} \times 50.0 \, \text{cm}\)
- Resistivity of carbon at \(20^\circ C\): \(\rho = 3.5 \times 10^{-5} \, \Omega \cdot \text{m}\)

### Part (i): Resistance between the two square ends

1. **Identify the dimensions for the calculation**:
- Length \(L = 50 \, \text{cm} = 50 \times 10^{-2} \, \text{m} = 0.50 \, \text{m}\)
- Area \(A = 1.0 \, \text{cm} \times 1.0 \, \text{cm} = 1.0 \times 10^{-4} \, \text{m}^2\)

2. **Use the formula for resistance**:
\[ R = \frac{\rho L}{A} \]

3. **Substitute the values into the formula**:
\[ R = \frac{3.5 \times 10^{-5} \, \Omega \cdot \text{m} \times 0.50 \, \text{m}}{1.0 \times 10^{-4} \, \text{m}^2} \]

4. **Calculate the resistance**:
\[ R = \frac{3.5 \times 10^{-5} \times 0.50}{1.0 \times 10^{-4}} = \frac{1.75 \times 10^{-5}}{1.0 \times 10^{-4}} = 0.175 \, \Omega \]

### Part (ii): Resistance between the two opposing rectangular faces

1. **Identify the dimensions for the calculation**:
- Length \(L = 1.0 \, \text{cm} = 1.0 \times 10^{-2} \, \text{m}\)
- Area \(A = 50.0 \, \text{cm} \times 1.0 \, \text{cm} = 50.0 \times 10^{-4} \, \text{m}^2\)

2. **Use the formula for resistance**:
\[ R = \frac{\rho L}{A} \]

3. **Substitute the values into the formula**:
\[ R = \frac{3.5 \times 10^{-5} \, \Omega \cdot \text{m} \times 0.01 \, \text{m}}{50.0 \times 10^{-4} \, \text{m}^2} \]

4. **Calculate the resistance**:
\[ R = \frac{3.5 \times 10^{-5} \times 0.01}{50.0 \times 10^{-4}} = \frac{3.5 \times 10^{-7}}{50.0 \times 10^{-4}} = \frac{3.5 \times 10^{-7}}{5.0 \times 10^{-3}} = 7.0 \times 10^{-5} \, \Omega \]

### Final Answers:
- (i) Resistance between the two square ends: \(0.175 \, \Omega\)
- (ii) Resistance between the two opposing rectangular faces: \(7.0 \times 10^{-5} \, \Omega\)