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

The thermal energy (heat) developed in a resistor is given by:

$$ H = I^2 R t $$

With $$I = 4$$ A and time $$t = 10$$ s, the thermal energy is $$H$$.

When the current is increased to 16 A (keeping the same resistor and same time):

$$ H' = (16)^2 R \times 10 = 256 R \times 10 $$

The ratio:

$$ \frac{H'}{H} = \frac{(16)^2}{(4)^2} = \frac{256}{16} = 16 $$

Therefore, the thermal energy developed is $$16H$$.

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