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A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11 V is connected across it is:
$$P_1 = I^2 R \implies R = \frac{P_1}{I^2}$$
$$R = \frac{4.4}{(2 \times 10^{-3})^2} = \frac{4.4}{4 \times 10^{-6}} = 1.1 \times 10^6\ \Omega$$
$$P_2 = \frac{V^2}{R}$$
$$P_2 = \frac{11^2}{1.1 \times 10^6} = \frac{121}{1.1 \times 10^6} = 110 \times 10^{-6} = 11 \times 10^{-5}\text{ W}$$
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