Which of the following statement is false

Options

A. Heat produced in a conductor is proportional to its resistance
B. Heat produced in a conductor is proportional to the square of the current
C. Heat produced in a conductor is proportional to charge
D. Heat produced in a conductor is proportional to the time for which current is passed

Answer

To determine which statement is false regarding the heating and chemical effects of current, let's analyze each option step by step.

### Step 1: Analyze the First Statement
**Statement:** Heat produced in a conductor is proportional to resistance.

**Analysis:**
The power (P) generated in a conductor due to current (I) flowing through it can be expressed as:
\[ P = I^2 R \]
Where:
- \( P \) is the power (or heat produced),
- \( I \) is the current,
- \( R \) is the resistance.

From this equation, we see that power (and thus heat) is directly proportional to resistance when current is constant.

**Conclusion:** This statement is **true**.

### Step 2: Analyze the Second Statement
**Statement:** Heat produced in a conductor is proportional to the square of the current.

**Analysis:**
Using the same equation \( P = I^2 R \), we can see that the power is indeed proportional to the square of the current when resistance is constant.

**Conclusion:** This statement is **true**.

### Step 3: Analyze the Third Statement
**Statement:** Heat produced in a conductor is proportional to charge.

**Analysis:**
Heat produced in a conductor is related to current and time. The relationship can be expressed as:
\[ Q = I \cdot t \]
Where:
- \( Q \) is the charge,
- \( I \) is the current,
- \( t \) is the time.

While heat is related to current, it is not directly proportional to charge. Current is defined as the rate of flow of charge. Therefore, saying heat is proportional to charge is misleading.

**Conclusion:** This statement is **false**.

### Step 4: Analyze the Fourth Statement
**Statement:** Heat produced in a conductor is proportional to the time for which current is passed.

**Analysis:**
From the equation for power, we can derive that:
\[ H = P \cdot t = I^2 R \cdot t \]
This shows that the heat produced is indeed proportional to the time for which the current flows, assuming constant current and resistance.

**Conclusion:** This statement is **true**.

### Final Conclusion
The false statement among the options is the third statement: "Heat produced in a conductor is proportional to charge."

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