A resistor of resistance R is connected to an ideal battery. If the value of R is decreased,the power dissipated in the resistor will

Answer

To solve the problem of how the power dissipated in a resistor changes when its resistance is decreased while connected to an ideal battery, we can follow these steps:

### Step 1: Understand the relationship between power, voltage, and resistance
The power \( P \) dissipated in a resistor can be expressed using the formula:
\[ P = \frac{V^2}{R} \]
where:
- \( P \) is the power,
- \( V \) is the voltage across the resistor, and
- \( R \) is the resistance of the resistor.

### Step 2: Analyze the effect of decreasing resistance
From the formula \( P = \frac{V^2}{R} \), we can see that power is inversely proportional to resistance \( R \). This means that if the resistance \( R \) decreases, the power \( P \) will increase, provided that the voltage \( V \) remains constant.

### Step 3: Conclude the effect on power
Since the resistor is connected to an ideal battery, the voltage \( V \) across the resistor remains constant. Therefore, if we decrease the value of \( R \), the power \( P \) dissipated in the resistor will increase.

### Final Answer
Thus, the power dissipated in the resistor will **increase** when the resistance \( R \) is decreased.

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