A Parallel Plate Capacitor Is Connected to a Battery and Charged

question 52

Multiple Choice

A parallel plate capacitor is connected to a battery and charged to voltage V. Leah says that the charge on the plates will decrease if the distance between the plates is increased while they are still connected to the battery. Gertie says that the charge will remain the same. Which one, if either, is correct, and why?

• A) Gertie, because the maximum voltage is determined by the battery.
• B) Gertie, because the capacitance of the capacitor does not change.
• C) Leah, because the capacitance decreases when the plate separation is increased.
• D) Leah, because the capacitance increases when the plate separation is increased.
• E) Neither, because the charge increases when the plate separation is increased.

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Definitions:

Utility Function

An economic tool used to encode a consumer's preference orderings over a set of alternatives into a real-valued function. (Duplicate rephrase)

Income

Funds obtained regularly as a result of employment or from returns on investments.

Cobb-Douglas Utility Function

A form of utility function that represents preferences of consumers for various goods, showcasing how they allocate their spending based on the utility derived from each good, typically in the form of \(U(x,y) = x^a y^b\) where \(x\) and \(y\) are quantities of goods and \(a\) and \(b\) are positive constants.

Inverse Demand Function

A mathematical function that expresses price as a function of quantity demanded, illustrating how the price necessary to sell a given quantity changes.