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, we need to determine the increase in power dissipated in a resistor when the current through it is increased by 100%.

### Step-by-Step Solution:

1. **Understanding Power Dissipation**:
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 through the resistor be \( I \). The initial power \( P_{\text{old}} \) can be expressed as:
\[ P_{\text{old}} = I^2 R \]

3. **Increasing Current by 100%**:
If the current is increased by 100%, the new current \( I_{\text{new}} \) will be:
\[ I_{\text{new}} = I + 100\% \text{ of } I = I + I = 2I \]

4. **New Power Calculation**:
Now, we calculate the new power \( P_{\text{new}} \) with the new current:
\[ P_{\text{new}} = (I_{\text{new}})^2 R = (2I)^2 R = 4I^2 R \]

5. **Calculating Increase in Power**:
The increase in power \( \Delta P \) is given by:
\[ \Delta P = P_{\text{new}} - P_{\text{old}} = 4I^2 R - I^2 R \]
Simplifying this gives:
\[ \Delta P = 3I^2 R \]

6. **Expressing Increase in Percentage**:
The increase in power can also be expressed as a percentage of the old power:
\[ \text{Percentage Increase} = \left( \frac{\Delta P}{P_{\text{old}}} \right) \times 100 = \left( \frac{3I^2 R}{I^2 R} \right) \times 100 = 300\% \]

### Final Answer:
The increase in power dissipated when the current is increased by 100% is \( 3I^2 R \) or \( 300\% \) of the old power.