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.

1. With the capacitor connected to the battery, inserting a dielectric with κ will increase C.
2. With the capacitor connected to the battery, decreasing d increases C.
3. After being disconnected from the battery, decreasing d increases U.
4. With the capacitor connected to the battery, decreasing d decreases Q.
5. With the capacitor connected to the battery, inserting a dielectric with κ will decrease U.
6. After being disconnected from the battery, inserting a dielectric with κ will decrease V.

Answer 1

Solution : 1. True, the capacitor connected to the battery, inserting a dielectric with k will increase C.

Because , capcitance will increase k times.. By formula, , we can see C is directly proportional to k.

2. True, the capacitor connected to the battery, decreasing d increases C. because , C is inversely proportional to d.

3. False, after being disconnected from the battery, decreasing d increases U.

Because, Q remain same, and so, as therefore . So U also decreases, by decreasing d.

4. False, the capacitor connected to the battery, decreasing d decreases Q.

Because Q = C V , potential remain same across capacitor by battery, and capacitance increases by decreasing d . so, Q also increases by decreasing d.

5. False, the capacitor connected to the battery, inserting a dielectric with κ will decrease U.

Because, across capacitor will remain same as V. so . , as C is directly proportional to k, therefore, U will increase by inserting a dielectric k into a capacitor.

6. True, after disconnecting the battery , charge will remain same. by inserting a dielectric k , capacitance will increase, and potenial V decreases, , by , V is inversely proportional to Capacitance C.