Review Conceptual Example 11 before attempting this problem. An empty capacitor is connected to a 9V battery and charged up. The capacitor is then disconnected from the battery, and a slab of dielectric material (k=3)is inserted between the plates.

(a) Find the amount by which the potential difference across the plates changes.

(b) Find the final potential difference.

The capacitance C triples since it is proportional to k, the charge stays the same and the voltage becomes Vo/3 = 3V.

The voltage drop is 6V

To solve this problem, we can use the concept of capacitance and the equation relating capacitance, voltage, and charge.

(a) To find the amount by which the potential difference across the plates changes, we need to determine the initial potential difference across the plates and the final potential difference after inserting the dielectric material.

The initial potential difference across the plates is equal to the voltage of the battery, which is 9V.

When the dielectric material is inserted between the plates, the capacitance of the capacitor increases due to the presence of the dielectric material. The capacitance of a capacitor with a dielectric material is given by the equation:

C' = k * C,

where C' is the new capacitance, k is the dielectric constant, and C is the original capacitance without the dielectric material.

Since the capacitor was initially empty, it had no charge. Therefore, the initial capacitance C is zero.

From the given information, the dielectric constant k is 3. Hence, the new capacitance C' is 3 * 0, which is also zero.

Therefore, the amount by which the potential difference across the plates changes is zero.

(b) The final potential difference across the plates can be found using the formula:

V' = (Q' / C'),

where V' is the final potential difference, Q' is the final charge, and C' is the new capacitance.

Since the dielectric material is inserted after charging the capacitor, the charge remains constant.

Therefore, Q' is equal to zero.

The new capacitance C' is also zero because the dielectric material increases the capacitance, but there was zero initial capacitance.

As a result, the final potential difference V' is undefined, as dividing zero charge by zero capacitance yields an indeterminate value.

In summary:

(a) The amount by which the potential difference across the plates changes is zero.
(b) The final potential difference is undefined.