Answer :
Final answer:
The voltage can be calculated using the relation V = √(P × R). After substituting the given values, the correct battery voltage is 0.6 V, which is not listed in the provided options. There might be a mistake in the question or options given.
Explanation:
To find the battery voltage given a 12 Ω resistor dissipates a power of 30 mW, we use the formula P = V^2 / R, where P is power, V is voltage, and R is resistance. In this case, the power P is 30 mW or 0.030 W (since 1 mW = 0.001 W), and the resistor R is 12 Ω.
Finding the voltage involves rearranging the formula to solve for V, which gives V = √(P × R). Plugging in the values, we get V = √(0.030 W × 12 Ω) = √(0.36 WΩ) = 0.6 V. However, since none of the options is 0.6 V, and we're likely looking at a multiple-choice question mistake or typo, you should inform your teacher or examiner to clarify the correct set of options or the power dissipation value.
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