Resistance increases with increases in temperature for

Options

A. Energy of activation `(E_(a))`
B. Collision frequency (Z)
C. Rate constant (k)
D. Both (B) and (C)

Explanation

To solve the question "Resistance increases with increases in temperature for," we need to analyze the options provided and determine which of them correctly explains why resistance increases with temperature.

### Step-by-Step Solution:

1. **Understanding Resistance and Temperature Relationship**:
- Resistance in a conductor typically increases with an increase in temperature. This is primarily due to the increased thermal motion of the electrons, which leads to more frequent collisions among them.

2. **Option 1: Energy of Activation**:
- The energy of activation (Ea) is the minimum energy required for a reaction to occur. As temperature increases, the fraction of molecules that have kinetic energy greater than the activation energy also increases. However, this does not directly relate to the increase in resistance. Therefore, this option is not correct.

3. **Option 2: Collision Frequency**:
- Collision frequency refers to the number of collisions per unit time between reactant particles. When temperature increases, the kinetic energy of the particles increases, leading to more frequent and effective collisions. This increased collision frequency can lead to an increase in resistance. Thus, this option is correct.

4. **Option 3: Rate Constant**:
- The rate constant (k) is related to the speed of a reaction. According to the Arrhenius equation, as temperature increases, the rate constant generally increases, which means that reactions occur faster. However, this does not imply that resistance increases with temperature. Therefore, this option is not directly related to the increase in resistance.

5. **Option 4: Both B and C**:
- Since option 2 (Collision Frequency) is correct and option 3 (Rate Constant) does not directly support the increase in resistance, option 4, which states "both B and C," is also incorrect.

### Conclusion:
The correct answer to the question is **Option 2: Collision Frequency**. Resistance increases with an increase in temperature primarily due to the increase in collision frequency among the electrons in the conductor.