Which of the following statements is/are correct?

Options

A. Resistivity of electrolytes decreases on increasing temperature
B. Resistance of mercury falls on decreasing its temperature
C. When joined in series, a 40 W bulb glows more than a 60 W bulb
D. Resistance of a 40 W bulb is less than the resistance of a 60 W bulb

Answer

To determine which statements are correct, let's analyze each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1:** The resistivity of the electrolyte decreases on increasing the temperature.

**Explanation:**
Resistivity (ρ) is defined as the resistance of a material per unit length and cross-sectional area. For most materials, especially conductors, resistivity decreases with an increase in temperature. This is because the increased thermal energy allows charge carriers to move more freely, thus reducing resistivity.

**Conclusion:** This statement is **correct**.

### Step 2: Analyze Statement 2
**Statement 2:** The resistance of mercury falls on decreasing its temperature.

**Explanation:**
Resistance (R) is given by the formula \( R = \frac{\rho L}{A} \), where ρ is resistivity, L is the length, and A is the cross-sectional area. For mercury, as the temperature decreases, its resistivity (ρ) decreases. Since resistance and resistivity are directly proportional, a decrease in temperature leads to a decrease in resistivity, which in turn leads to a decrease in resistance.

**Conclusion:** This statement is **correct**.

### Step 3: Analyze Statement 3
**Statement 3:** When joined in series, a 40 Watt bulb glows more than a 60 Watt bulb.

**Explanation:**
In a series circuit, the same current flows through all components. The brightness of a bulb is related to the power it dissipates. A 60 Watt bulb is designed to consume more power than a 40 Watt bulb under the same voltage. Therefore, the 60 Watt bulb will glow brighter than the 40 Watt bulb when connected in series.

**Conclusion:** This statement is **incorrect**.

### Step 4: Analyze Statement 4
**Statement 4:** The resistance of a 40W bulb will be less than the resistance of a 60W bulb.

**Explanation:**
Power (P) is related to resistance (R) and voltage (V) by the formula \( P = \frac{V^2}{R} \). Rearranging gives \( R = \frac{V^2}{P} \). Since the power of the 40W bulb is less than that of the 60W bulb, the resistance of the 40W bulb will be greater than that of the 60W bulb.

**Conclusion:** This statement is **incorrect**.

### Final Summary of Correct Statements
- **Correct Statements:** 1 and 2
- **Incorrect Statements:** 3 and 4