A rectangular conducting cube (resistivity `rho` ) has dimensions `l xx bxx h.` When current is passed through the length side, the resistance offered by the cube is

Options

A. `(rhol )/(bh)`
B. `(rhob )/(hl)`
C. `(rho h)/(lb)`
D. `rho (lb)/(h ^(2))`

Explanation

To find the resistance offered by a rectangular conducting cube when current is passed through the length side, we can use the formula for resistance in terms of resistivity, length, and cross-sectional area. Here are the steps to derive the resistance:

### Step-by-Step Solution:

1. **Understand the Dimensions**:
The cube has dimensions \( l \) (length), \( b \) (breadth), and \( h \) (height). When current is passed through the length side, the current flows along the length \( l \).

2. **Identify the Formula for Resistance**:
The resistance \( R \) of a conductor is given by the formula:
\[ R = \frac{\rho L}{A} \]
where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the conductor through which the current flows,
- \( A \) is the cross-sectional area perpendicular to the current flow.

3. **Determine the Length and Area**:
- Since the current is flowing through the length \( l \), we have \( L = l \).
- The cross-sectional area \( A \) when current flows through the length side is the area of the face perpendicular to the length, which is given by:
\[ A = b \times h \]

4. **Substitute the Values into the Formula**:
Now, substituting \( L \) and \( A \) into the resistance formula:
\[ R = \frac{\rho l}{b \times h} \]

5. **Final Expression for Resistance**:
Therefore, the resistance offered by the cube when current is passed through the length side is:
\[ R = \frac{\rho l}{b h} \]