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------------------------------------------------ A constant current of 913 mA flows through a light bulb. During a 45-minute period, the light bulb gives off 61 kJ of energy in the form of light and heat. What is the voltage across the light bulb?

a) 68 V
b) 42 V
c) 27 V
d) 35 V

To find the voltage across the light bulb, the power was calculated using the given energy and time, resulting in 22.59 W. Then, using the current of 0.913 A, the voltage was computed using Ohm's law, with the closest option being 27 V. So correct option is C.

Explanation:

The voltage across the light bulb can be found using the relationship between power (P), current (I), and voltage (V), which is given by P = IV, where power is in watts (W), current is in amperes (A), and voltage is in volts (V). First, we need to convert 61 kJ of energy released by the light bulb into watts considering the time is 45 minutes. The energy in joules (J) is 61,000 J and the time in seconds (t) is 45 minutes \\times 60 seconds/minute = 2,700 seconds. Using P = energy/time, we get P = 61,000 J / 2,700 s = 22.59 W.

Now, since we have the power and the current, we can find the voltage using the equation P = IV. The given current is 0.913 A (913 mA). Rearranging the equation for voltage gives us V = P / I, which results in V = 22.59 W / 0.913 A = 24.74 V. Although this calculated voltage is not listed in the multiple-choice options provided, by examining the process, it is clear that among the given options (68 V, 42 V, 27 V, 35 V), option c) 27 V is the closest to the calculated voltage. Thus, based on a likely rounding discrepancy, option c) 27 V is the correct option to choose.