Question

An RLC circuit has a resistance of (1.93x10^2)ohms , an inductance of (1.74x10¹ ) mH, and a capacitance of (3.29x10¹ ) nF. At time t = 0 the charge on the capacitor is (2.6x10¹ ) micro C and there is no current flowing. What is the energy stored in the capacitor after two complete cycles?

Answer 1

The energy stored in the capacitor after two complete cycles in a lossless RLC circuit remains the same as the initial energy, which can be calculated using the provided charge and capacitance values.

Step-by-step explanation:

The energy stored in a capacitor is given by the formula ½ CV² where C is the capacitance and V is the voltage across the capacitor. The charge on the capacitor Q is related to the voltage by Q = CV. Hence, the energy can also be expressed as ½ Q²/C. After two complete cycles in an RLC circuit, without energy losses due to resistance, the energy stored in the capacitor would be the same as initially since the energy oscillates between the capacitor and inductor.

Using the charge given (2.6×10± microCoulombs) and the capacitance (3.29×10± nF), the initial energy in the capacitor is calculated as follows:

E = ½ (2.6×10± × 10⁻¶ C)² / (3.29×10± × 10⁻¹ F)

E = 0.5 × (2.6×10±)² × 10⁻¶/(3.29×10±×10⁻¹) Joules

Therefore, assuming no energy is lost to resistance, the energy stored in the capacitor after two complete cycles is the same as the initial energy.