A series RLC circuit, with R = 200ohms, L = 0.1H and C = 10µF, has an initial charge on the capacitor of Q = 2.67mC. A switch is closed at t=0 allowing the capacitor to discharge through the R and L mentioned earlier.The circuit is1. Overdamped2. Underdamped3. Critically damped
Question
A series RLC circuit, with R = 200ohms, L = 0.1H and C = 10µF, has an initial charge on the capacitor of Q = 2.67mC. A switch is closed at t=0 allowing the capacitor to discharge through the R and L mentioned earlier.The circuit is1. Overdamped2. Underdamped3. Critically damped
Solution
To determine whether the circuit is overdamped, underdamped, or critically damped, we need to calculate the damping factor (ζ). The damping factor is given by the formula:
ζ = R / (2 * sqrt(L/C))
where: R = resistance = 200 ohms L = inductance = 0.1 H C = capacitance = 10 µF = 10 * 10^-6 F
Substituting these values into the formula, we get:
ζ = 200 / (2 * sqrt(0.1/(10 * 10^-6)))
Solving this, we get:
ζ = 200 / (2 * sqrt(10^7)) ζ = 200 / (2 * 10^3.5) ζ = 200 / 6324.555 ζ = 0.0316
The damping factor ζ < 1, which means the circuit is underdamped.
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