Given, energy dissipated by a resistor, H = 10 mJ = 10 $$\times$$ 10^$$-$$3 J

Time, t = 1 s

Electric current, I = 2 mA = 2 $$\times$$ 10^$$-$$3 A

Resistance, R = ?

According to Joule's law of heating,

H = I²Rt

$$ \Rightarrow R = {H \over {{I^2}T}}$$ ....... (i)

Substituting the given values in Eq. (i), we get

$$R = {{10 \times {{10}^{ - 3}}} \over {{{(2 \times {{10}^{ - 3}})}^2} \times 1}}$$

$$ \Rightarrow R = {{{{10}^{ - 2}}} \over {4 \times {{10}^{ - 6}}}} \Rightarrow R = 0.25 \times {10^4}$$

$$ \Rightarrow R = 2500\,\Omega $$