Final answer:
The energy stored in a 10.0-µF capacitor charged to 9.00 × 10³ V is 405 J. The amount of stored charge in the capacitor is 90 mC.
Step-by-step explanation:
Energy Stored in a Capacitor
The energy stored in a capacitor can be calculated using the formula:
E = ½ × C × V²
where E is the energy in joules (J), C is the capacitance in farads (F), and V is the voltage in volts (V). In the case of a 10.0-µF capacitor charged to 9.00 × 10³ V, we substitute the values into the formula:
E = ½ × 10.0 × 10 µF × (9.00 × 10³ V)²
Therefore, the energy stored is:
E = ½ × 10.0 × 10 µF× (9.00 × 10³)² = ½ × 10.0 × 10µF × 81.0 × 10µF = 405 J
Stored Charge in a Capacitor
The charge Q stored in a capacitor is calculated using the formula:
Q = C × V
For the given values, the amount of stored charge is:
Q = 10.0 × 10⁻µF × 9.00 × 10³ V = 90 mC