If the current through a resistor is increased by 50%, the increase in power dissipated will be (assume the temperature remains constant)

Options

A. 2.25
B. 2
C. 2.5
D. 1.25

Explanation

To solve the problem of how much the power dissipated in a resistor increases when the current is increased by 50%, 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. **Determine the New Current**:
If the current is increased by 50%, the new current \( I' \) can be calculated as:
\[ I' = I + 0.5I = 1.5I = \frac{3}{2}I \]

3. **Calculate the New Power**:
Substitute the new current \( I' \) into the power formula:
\[ P' = (I')^2 R = \left(\frac{3}{2}I\right)^2 R = \frac{9}{4}I^2 R \]

4. **Calculate the Original Power**:
The original power \( P \) is:
\[ P = I^2 R \]

5. **Find the Increase in Power**:
The increase in power \( \Delta P \) is given by:
\[ \Delta P = P' - P = \frac{9}{4}I^2 R - I^2 R \]
Simplifying this:
\[ \Delta P = \frac{9}{4}I^2 R - \frac{4}{4}I^2 R = \frac{5}{4}I^2 R \]

6. **Calculate the Percentage Increase in Power**:
The percentage increase in power is calculated as:
\[ \text{Percentage Increase} = \left(\frac{\Delta P}{P}\right) \times 100 = \left(\frac{\frac{5}{4}I^2 R}{I^2 R}\right) \times 100 \]
This simplifies to:
\[ \text{Percentage Increase} = \frac{5}{4} \times 100 = 125\% \]

### Final Answer:
The increase in power dissipated will be **125%**.