All the edges of a block with parallel faces are unequal. Its longest edge is twice its shortest edge. The ratio of the maximum to minimum resistance between parallel faces is.

Options

A. 2
B. 4
C. 8
D. independent unless the length of the liquid of the third edge is specified.

Explanation

To solve the problem, we need to find the ratio of the maximum to minimum resistance between the parallel faces of a block with unequal edges, where the longest edge is twice the shortest edge.

### Step-by-Step Solution:

1. **Define the Dimensions**:
- Let the shortest edge be \( h \).
- Since the longest edge is twice the shortest edge, let the longest edge \( l = 2h \).
- Let the third edge (breadth) be \( b \), which is not specified but is different from \( h \) and \( l \).

2. **Identify the Resistances**:
- The resistances between the parallel faces can be calculated using the formula \( R = \frac{\rho \cdot L}{A} \), where \( R \) is resistance, \( \rho \) is resistivity, \( L \) is the length of the current path, and \( A \) is the cross-sectional area.

3. **Calculate Resistance \( R_1 \)**:
- For resistance \( R_1 \) between faces with area \( h \times b \) and length \( l \):
\[ R_1 = \frac{\rho \cdot l}{h \cdot b} \]
- Substituting \( l = 2h \):
\[ R_1 = \frac{\rho \cdot 2h}{h \cdot b} = \frac{2\rho}{b} \]

4. **Calculate Resistance \( R_2 \)**:
- For resistance \( R_2 \) between faces with area \( l \times h \) and length \( b \):
\[ R_2 = \frac{\rho \cdot b}{l \cdot h} \]
- Substituting \( l = 2h \):
\[ R_2 = \frac{\rho \cdot b}{2h \cdot h} = \frac{\rho}{2h} \]

5. **Calculate Resistance \( R_3 \)**:
- For resistance \( R_3 \) between faces with area \( l \times b \) and length \( h \):
\[ R_3 = \frac{\rho \cdot h}{l \cdot b} \]
- Substituting \( l = 2h \):
\[ R_3 = \frac{\rho \cdot h}{2h \cdot b} = \frac{\rho}{2b} \]

6. **Identify Maximum and Minimum Resistance**:
- From the calculated resistances:
- \( R_1 = \frac{2\rho}{b} \)
- \( R_2 = \frac{\rho}{2h} \)
- \( R_3 = \frac{\rho}{2b} \)
- The maximum resistance \( R_{max} = R_1 \) and the minimum resistance \( R_{min} = R_3 \).

7. **Calculate the Ratio of Maximum to Minimum Resistance**:
\[ \text{Ratio} = \frac{R_{max}}{R_{min}} = \frac{R_1}{R_3} = \frac{\frac{2\rho}{b}}{\frac{\rho}{2b}} = \frac{2\rho}{b} \cdot \frac{2b}{\rho} = 4 \]

### Final Answer:
The ratio of the maximum to minimum resistance between the parallel faces is \( 4 \).