The H amount of thermal energy is developed by a resistor in 10 s when a current of 4A is passed through it. If the current is increased to 16A, the thermal energy developed by the resistor in 10 s will be:

Options

A. `H/4`
B. `H`
C. `4H`
D. `16 H`

Answer

To solve the problem, we need to determine the thermal energy developed by a resistor when the current is increased. We can use the formula for thermal energy developed by a resistor, which is given by:

\[ H = I^2 R t \]

Where:
- \( H \) is the thermal energy,
- \( I \) is the current,
- \( R \) is the resistance,
- \( t \) is the time.

### Step 1: Calculate the thermal energy for the first scenario
Given:
- Current \( I_1 = 4 \, A \)
- Time \( t = 10 \, s \)
- Thermal energy developed \( H_1 = H \)

Using the formula:
\[ H_1 = I_1^2 R t \]
\[ H = (4^2) R (10) \]
\[ H = 16 R \cdot 10 \]
\[ H = 160 R \]

### Step 2: Calculate the thermal energy for the second scenario
Now, we need to find the thermal energy when the current is increased to \( I_2 = 16 \, A \):
\[ H_2 = I_2^2 R t \]
\[ H_2 = (16^2) R (10) \]
\[ H_2 = 256 R \cdot 10 \]
\[ H_2 = 2560 R \]

### Step 3: Determine the ratio of the thermal energies
To find out how much more thermal energy is developed when the current is increased, we can take the ratio of \( H_2 \) to \( H_1 \):
\[ \frac{H_2}{H_1} = \frac{2560 R}{160 R} \]
The \( R \) cancels out:
\[ \frac{H_2}{H_1} = \frac{2560}{160} = 16 \]

### Conclusion
Thus, when the current is increased from 4 A to 16 A, the thermal energy developed by the resistor in 10 seconds will be 16 times the original amount of thermal energy \( H \).

The final answer is:
\[ H_2 = 16H \]