Device power consumption is determined by the applied voltage and the device's resistance.
The power formula is:
\(P=\frac{V^2}{R}\).
The bulb's resistance R can be calculated from its rated voltage and power, which are 200 V and 100 W, respectively.
Using the formula
\(R = \frac{V_{\text{rated}}^2}{P_{\text{rated}}} = \frac{200^2}{100} = 400 \, \Omega\)
Next, we calculate the power consumed at an applied voltage of 160 V using the same formula:
\(P = \frac{160^2}{400} = \frac{25600}{400} = 64 \, W\)
Therefore, the bulb consumes 64 W when connected to a 160 V power supply.