The sides of rectangular block are 2 cm, 3 cm ad 4 cm. The ratio of the maximum to minimum resistance between its parallel faces is

Options

A. 3
B. 4
C. 2
D. 1

Explanation

To find the ratio of the maximum to minimum resistance between the parallel faces of a rectangular block with sides 2 cm, 3 cm, and 4 cm, we can follow these steps:

### Step 1: Identify the dimensions of the rectangular block
The sides of the rectangular block are given as:
- Length (A) = 4 cm
- Width (B) = 3 cm
- Height (C) = 2 cm

### Step 2: Determine the maximum resistance
The maximum resistance occurs when the length of the current path is the longest, which is along the longest side (A = 4 cm). The area of the cross-section will be the product of the other two dimensions (B and C).

- Maximum resistance (R_max) can be calculated using the formula:
\[ R_{max} = \frac{\rho L_{max}}{A_{min}} \]
Where:
- \( L_{max} = 4 \) cm
- \( A_{min} = B \times C = 3 \times 2 = 6 \) cm²
- \( \rho \) is the resistivity of the material (which will cancel out later).

Thus,
\[ R_{max} = \frac{\rho \cdot 4}{6} = \frac{2\rho}{3} \]

### Step 3: Determine the minimum resistance
The minimum resistance occurs when the length of the current path is the shortest, which is along the shortest side (C = 2 cm). The area of the cross-section will be the product of the other two dimensions (A and B).

- Minimum resistance (R_min) can be calculated using the formula:
\[ R_{min} = \frac{\rho L_{min}}{A_{max}} \]
Where:
- \( L_{min} = 2 \) cm
- \( A_{max} = A \times B = 4 \times 3 = 12 \) cm²

Thus,
\[ R_{min} = \frac{\rho \cdot 2}{12} = \frac{\rho}{6} \]

### Step 4: Calculate the ratio of maximum to minimum resistance
Now we can find the ratio of maximum resistance to minimum resistance:
\[ \text{Ratio} = \frac{R_{max}}{R_{min}} = \frac{\frac{2\rho}{3}}{\frac{\rho}{6}} \]

### Step 5: Simplify the ratio
Cancelling out \( \rho \) from the numerator and denominator:
\[ \text{Ratio} = \frac{2}{3} \times 6 = \frac{12}{3} = 4 \]

### Final Answer
The ratio of the maximum to minimum resistance between the parallel faces of the rectangular block is **4**.

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