A capacitor is charged to a potential of 12V and then disconnected from the battery. If the plate area is doubled, what will be the new potential difference? (2022)
Practice Questions
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Q1
A capacitor is charged to a potential of 12V and then disconnected from the battery. If the plate area is doubled, what will be the new potential difference? (2022)
6V
12V
24V
It cannot be determined
Once disconnected, the charge remains constant. Doubling the area increases capacitance but does not change the potential difference since the charge is fixed.
Questions & Step-by-step Solutions
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Q
Q: A capacitor is charged to a potential of 12V and then disconnected from the battery. If the plate area is doubled, what will be the new potential difference? (2022)
Solution: Once disconnected, the charge remains constant. Doubling the area increases capacitance but does not change the potential difference since the charge is fixed.
Steps: 7
Step 1: Understand that a capacitor stores electrical charge and has a certain voltage (potential difference) when connected to a battery.
Step 2: When the capacitor is charged to 12V and then disconnected from the battery, the charge on the capacitor plates remains constant.
Step 3: Know that the capacitance (C) of a capacitor is related to its plate area (A) and the distance between the plates (d) by the formula: C = ε * (A/d), where ε is the permittivity of the material between the plates.
Step 4: If the plate area (A) is doubled, the capacitance (C) increases because capacitance is directly proportional to the area.
Step 5: However, since the capacitor is disconnected, the total charge (Q) on the plates remains the same. The relationship between charge, capacitance, and voltage is given by the formula: Q = C * V.
Step 6: Since the charge (Q) is constant and capacitance (C) has increased, the voltage (V) must decrease to keep the equation balanced.
Step 7: Therefore, even though the capacitance increases, the potential difference (voltage) across the capacitor does not change from the original 12V because the charge is fixed.
