Question

In the given scenario, what is the resonant frequency (f0) for the circuit described, and at this frequency, what is the expression for the voltage across just the capacitor (vc(t))?

a) Resonant frequency (f0): Determined from equations (2) and (3)
Voltage across capacitor (vc(t)): Not specified
b) Resonant frequency (f0): Not provided
Voltage across capacitor (vc(t)): Determined from equations (2) and (3)
c) Resonant frequency (f0): Determined from equations (2) and (3)
Voltage across capacitor (vc(t)): Express as specified in the equations
d) Resonant frequency (f0): Not provided
Voltage across capacitor (vc(t)): Not specified

Answer 1

The resonant frequency (f0) for an RLC circuit is found using the formula f0 = 1 / (2π√(LC)) and the voltage across the capacitor (vc(t)) at resonance can be expressed using the current and capacitive reactance.

Step-by-step explanation:

The resonant frequency (f0) of an RLC circuit is determined by the values of the resistance (R), inductance (L), and capacitance (C) in the series. The formula to find the resonant frequency is f0 = 1 / (2π√(LC)), where L is the inductance in henrys (H) and C is the capacitance in farads (F). At the resonant frequency, the impedance of the circuit is minimized and the circuit would resonate at its natural frequency if undriven. The voltage across the capacitor (vc(t)) can be expressed using the current in the circuit and the capacitive reactance, which is inversely proportional to the frequency and capacitance (vc(t) = I(t) / (ωC)).