If the current `I` through a resistor is increased by `100%` (assume that temperature remains unchanged), the increase in power dissipated will be :

Options

A. `100%`
B. `200%`
C. `300%`
D. `400%`

Explanation

To solve the problem of how the power dissipated in a resistor changes when the current is increased by 100%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Power Formula**:
The power \( P \) dissipated in a resistor is given by the formula:
\[ P = I^2 R \]
where \( I \) is the current through the resistor and \( R \) is the resistance.

2. **Initial Power Calculation**:
Let the initial current be \( I \). The initial power \( P_1 \) can be expressed as:
\[ P_1 = I^2 R \]

3. **Determine the New Current**:
If the current is increased by 100%, the new current \( I' \) becomes:
\[ I' = I + 100\% \text{ of } I = I + I = 2I \]

4. **Calculate the New Power**:
Now, substituting the new current \( I' \) into the power formula, the new power \( P_2 \) becomes:
\[ P_2 = (2I)^2 R = 4I^2 R \]

5. **Calculate the Increase in Power**:
The increase in power \( \Delta P \) is given by the difference between the new power and the initial power:
\[ \Delta P = P_2 - P_1 = 4I^2 R - I^2 R = 3I^2 R \]

6. **Express the Increase as a Percentage**:
To find the percentage increase in power, we can use the formula:
\[ \text{Percentage Increase} = \left( \frac{\Delta P}{P_1} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{3I^2 R}{I^2 R} \right) \times 100 = 3 \times 100 = 300\% \]

### Final Answer:
The increase in power dissipated when the current is increased by 100% is **300%**.

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