Introduction:
When a conductor of resistance R, length L, thickness D, and resistivity r is cut into four equal parts, the resistivity of each part will change. To understand why this happens, we need to consider the factors that affect resistance and how they change when the conductor is divided.

Resistance and Resistivity:
Resistance (R) is a measure of how much a conductor opposes the flow of electric current. It depends on the resistivity (r) of the material, length (L) of the conductor, and its cross-sectional area (A). The relationship can be expressed using the formula R = (r * L) / A.

Changes in Length and Cross-sectional Area:
When the conductor is cut into four equal parts, both the length and cross-sectional area of each part change. Since the original conductor is divided into four equal parts, the length of each part will be L/4. The cross-sectional area of each part will also change since the original conductor's area is divided equally.

Changes in Resistivity:
The resistivity of a material is an intrinsic property that depends on the nature of the material itself. When the conductor is cut into four equal parts, the resistivity of each part remains the same as the original conductor.

Calculating New Resistance:
To calculate the new resistance of each part, we need to consider the changes in length and cross-sectional area. Since the length of each part is L/4 and the thickness remains the same, the new cross-sectional area will also be D. Using the formula mentioned earlier, we can calculate the new resistance of each part.

Conclusion:
When a conductor of resistance R, length L, thickness D, and resistivity r is cut into four equal parts, the resistivity of each part remains the same as the original conductor. However, the resistance of each part changes due to the changes in length and cross-sectional area. By considering these changes, we can calculate the new resistance using the formula R = (r * L/4) / D.