A parallel plate capacitor with plate separation d is connected to a battery. Th

Question

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery. For each statement below, select True or False.

True False  After being disconnected from the battery, decreasing d decreases C.
True False  With the capacitor connected to the battery, inserting a dielectric with will decrease C.
True False  With the capacitor connected to the battery, increasing d decreases Q.
True False  After being disconnected from the battery, inserting a dielectric with will increase V.
True False  With the capacitor connected to the battery, inserting a dielectric with will decrease U.
True False  After being disconnected from the battery, decreasing d increases U.

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Which statements are true for two oppositely charged, isolated parallel plates: C=capacitance, U=stored energy (Q and -Q = charge on the plates). Note: Isolated plates can not lose their charge.

True False  Inserting a dielectric decreases U.
True False  Inserting a dielectric increases Q.
True False  When the distance is halved, Q stays the same.
True False  Increasing the distance increases the Electric field.
True False  Inserting a dielectric increases C.
True False  When the distance is doubled, C increases.
True False  When the distance is doubled, U increases.

Explanation / Answer

After being disconnected from the battery, decreasing d decreases C. false because C is inversely proprotional to d

With the capacitor connected to the battery, inserting a dielectric with will decrease C. False beacause C is directly proportional to k

With the capacitor connected to the battery, increasing d decreases Q. True increasing d will decrease C and Q = CV so Q also decreases

After being disconnected from the battery, inserting a dielectric with will increase V.  False because Q =CV so insreting dielectric increase C and Q being constant so V decreases

With the capacitor connected to the battery, inserting a dielectric with will decrease U. False because U = 1/2 CV^2 = so inserting dileectric inreases C so U also increase

After being disconnected from the battery, decreasing d increases U. False beacuse Q constant and C increases as d decreases so  U = Q^2/2C so U DECREASES

using same concepts as we used above we can answer beolw questions as well. also Q remain cosntant

True Inserting a dielectric decreases U.
False  Inserting a dielectric increases Q.
True When the distance is halved, Q stays the same.
False  Increasing the distance increases the Electric field.
True Inserting a dielectric increases C.
True False  When the distance is doubled, C increases.
True False  When the distance is doubled, U increases.

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