A resistor develops 300 J of thermal energy in 15 s, when a current of 2 A is passed through it. If the current increases to 3 A, the energy developed in 10 s is __________ J

Explanation

To solve the problem, we will use the formula for the thermal energy (heat) developed in a resistor when a current flows through it. The formula is:

\[ H = I^2 R T \]

Where:
- \( H \) is the heat energy developed (in Joules),
- \( I \) is the current (in Amperes),
- \( R \) is the resistance (in Ohms),
- \( T \) is the time (in seconds).

### Step-by-Step Solution:

1. **Identify the given values for the first scenario**:
- Current \( I_1 = 2 \) A
- Time \( T_1 = 15 \) s
- Heat developed \( H_1 = 300 \) J

2. **Use the heat formula to express resistance \( R \)**:
\[ H_1 = I_1^2 R T_1 \]
Substituting the known values:
\[ 300 = (2^2) R (15) \]
\[ 300 = 4R \times 15 \]
\[ 300 = 60R \]
\[ R = \frac{300}{60} = 5 \, \Omega \]

3. **Identify the new values for the second scenario**:
- Current \( I_2 = 3 \) A
- Time \( T_2 = 10 \) s

4. **Use the heat formula again to find the new heat \( H_2 \)**:
\[ H_2 = I_2^2 R T_2 \]
Substituting the known values:
\[ H_2 = (3^2) R (10) \]
\[ H_2 = 9R \times 10 \]
\[ H_2 = 90R \]

5. **Substituting the value of \( R \)**:
\[ H_2 = 90 \times 5 = 450 \, J \]

### Final Answer:
The energy developed in 10 seconds when the current increases to 3 A is **450 J**.

---