A metallic resistor is connected across a battery.If the number of collisions if the free electrons with the lattice is somehow decreased in the resistor (for example,by cooling it ),the current will

Options

A. (a)increase
B. (b)decrease
C. (c ) remain constant
D. (d) become zero

Answer

To solve the question about the effect of decreased collisions of free electrons with the lattice in a metallic resistor connected to a battery, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Drift Velocity**:
- In a metallic conductor, free electrons move through the lattice structure of the metal. The movement of these electrons is affected by collisions with the lattice ions. When the number of collisions decreases, the drift velocity of the electrons increases.

2. **Relate Drift Velocity to Current**:
- The current (I) flowing through a conductor can be expressed by the formula:
\[ I = n \cdot e \cdot A \cdot v_d \]
where:
- \(I\) = current
- \(n\) = number of charge carriers per unit volume
- \(e\) = charge of an electron
- \(A\) = cross-sectional area of the conductor
- \(v_d\) = drift velocity of the electrons

3. **Analyze the Effect of Decreased Collisions**:
- If the number of collisions decreases (for example, by cooling the resistor), the drift velocity \(v_d\) will increase. Since the current is directly proportional to the drift velocity, an increase in \(v_d\) will lead to an increase in current \(I\).

4. **Conclusion**:
- Therefore, if the number of collisions of free electrons with the lattice decreases, the current will increase.

### Final Answer:
The current will **increase** (Option A).

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