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Question

In an LC circuit, the energy oscillates between:

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
 **Primary Concept**: Energy oscillation in LC circuits
 **Related Topics**: Electromagnetic oscillations, resonance, simple harmonic motion
 **Prerequisites**: Understanding of capacitance, inductance, electric and magnetic fields, energy storage in capacitors and inductors.
## SOLUTION PATHWAY
**Given Information**:
  An LC circuit (a circuit containing only an inductor and a capacitor).
  Energy is oscillating.
**Method & Steps**:
 1. Understand energy storage in capacitors and inductors.
  Reasoning: A capacitor stores energy in its electric field ($U_C = \frac{1}{2}CV^2 = \frac{1}{2}Q^2/C$), while an inductor stores energy in its magnetic field ($U_L = \frac{1}{2}LI^2$).
  Formula/Rule: $U_C = \frac{1}{2}CV^2$, $U_L = \frac{1}{2}LI^2$
 2. Analyze the energy transfer in an LC circuit.
  Working: In an LC circuit, when the capacitor is fully charged, the energy is entirely stored in the electric field of the capacitor. As the capacitor discharges, the current flows through the inductor, building up a magnetic field. The energy transfers from the electric field of the capacitor to the magnetic field of the inductor.  When the capacitor is fully discharged, all the energy is stored in the magnetic field of the inductor. The process then reverses, and the energy oscillates back and forth between the capacitor and inductor.
  Key Point:  No energy is lost (ideally) in this process, as there is no resistance in the circuit. The total energy remains constant.
 3. Identify the correct option.
  Result: The energy oscillates between the electric field of the capacitor and the magnetic field of the inductor.
  Verification: This is consistent with the principle of energy conservation in an ideal LC circuit.
 ## OPTION ANALYSIS
A :x: The energy is not simply oscillating between the capacitor and the inductor as components; it's the energy stored in their respective fields.
B :x: Resistors dissipate energy as heat; an ideal LC circuit has no resistor.
C :x: Similar to B, resistors are not present in an ideal LC circuit.
D ✓: This option correctly identifies the energy storage locations and the oscillatory nature of the energy transfer.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing the capacitor and inductor as the energy storage locations instead of their respective fields: Focus on the electric field in the capacitor and magnetic field in the inductor.
  2.Ignoring the oscillatory nature of energy transfer: Remember the energy sloshes back and forth between the two fields.
 **Quick Tips**:
  1.Visualize the energy transfer as a pendulum swinging: The potential energy (capacitor) converts to kinetic energy (inductor) and back.
  2.Remember the energy formulas for capacitors and inductors to understand the energy storage mechanism.

VENKATESWARARAO · Answer

The capacitor and the inductor

VENKATESWARARAO · Answer

The resistor and the capacitor

VENKATESWARARAO · Answer

The resistor and the inductor

VENKATESWARARAO · Answer

The correct Option is "The electric field of the capacitor and the magnetic field of the inductor"

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