Multiple Choice
What is the resonant frequency of an LC circuit consisting of a inductor paired with a capacitor?
30. Induction and Inductance
LC Circuits
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In an oscillating LC circuit in which the capacitance C = 4μF and the maximum voltage across the capacitor V = 1.50V, the maximum current measured across the inductor is 50mA. What is the angular frequency of this LC circuit?
A
69444444 rad/s
B
8333 rad/s
C
1521 rad/s
D
0.00012 rad/s
Verified step by step guidance1
Start by understanding that in an LC circuit, the energy oscillates between the capacitor and the inductor. The total energy in the circuit is conserved and can be expressed in terms of the maximum voltage across the capacitor and the maximum current through the inductor.
The energy stored in the capacitor at maximum voltage is given by the formula: \( E_C = \frac{1}{2} C V^2 \), where \( C \) is the capacitance and \( V \) is the maximum voltage.
The energy stored in the inductor at maximum current is given by the formula: \( E_L = \frac{1}{2} L I^2 \), where \( L \) is the inductance and \( I \) is the maximum current.
Since the energy is conserved, set the energy in the capacitor equal to the energy in the inductor: \( \frac{1}{2} C V^2 = \frac{1}{2} L I^2 \). Solve this equation for the inductance \( L \).
The angular frequency \( \omega \) of the LC circuit is given by the formula: \( \omega = \frac{1}{\sqrt{LC}} \). Use the value of \( L \) obtained from the previous step and the given capacitance \( C \) to calculate \( \omega \).
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