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An RLC circuit has L = 25 mH and C = 5.0 microF. It is found that the charge on the capacitor does not oscillate but instead decays exponentially to zero (overdamped). The circuit resistance must therefore be:

1. greater than or equal to 100*sqrt(2) Ohm
2. less than 100*sqrt(2) Ohm but greater than 50*sqrt(2) Ohm
3. less than 50*sqrt(2) Ohm but greater than 25*sqrt(2) Ohm
4. less than 25*sqrt(2) Ohm but greater than 0

Correct answer: greater than or equal to 100*sqrt(2) Ohm

Solution

An RLC circuit stops oscillating (becomes critically or over-damped) when R >= R_critical = 2*sqrt(L/C). Compute: L/C = (25*10⁻³)/(5.0*10⁻⁶) = 5000, sqrt(5000) = 50*sqrt(2). Thus R_critical = 2*50*sqrt(2) = 100*sqrt(2) Ohm. For no oscillation, R must be greater than or equal to 100*sqrt(2) Ohm.

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