An RLC circuit has an inductance of 25 mH and a capacitance of 5.0 $\mu$F. The charge on the capacitor does NOT oscillate but rather decays exponentially to zero. The resistance in the circuit must be:
A) greater than or equal to 20,000 $\Omega$
B) less than 20,000$\Omega$ but greater than 10,000 $\Omega$
C) less than 10,000 $\Omega$ but greater than 5,000 $\Omega$
D) less than 5,000 $\Omega$ but greater than 0
E) 0

Question

Quizplus · Accepted Answer

For the charge on the capacitor to decay exponentially without oscillation, the circuit must be overdamped. This occurs when the resistance is greater than or equal to the critical resistance, which is calculated using the formula R_c = 2 * sqrt(L/C). Substituting L = 25 mH and C = 5.0 μF, we find R_c = 2 * sqrt(0.025/0.000005) = 20,000 Ω. Thus, the resistance must be greater than or equal to 20,000 Ω.

An RLC Circuit Has an Inductance of 25 MH and a Capacitance