Final answer:
To make an RLC circuit with R = 50Ω and L = 1.5H overdamped, the capacitor value C must be less than 2400 μF according to the inequality derived from the damping factor condition.
Step-by-step explanation:
To determine the value of C that will make a sourceless series RLC (resistor, inductor, capacitor) circuit overdamped, we need to consider the damping factor, which depends on resistance R, inductance L, and capacitor value C. The damping factor (ζ) is given by ζ = R/(2*√(L/C)). For a circuit to be overdamped, the damping factor needs to be greater than 1, which implies that R > 2*√(L/C).
Given R = 50Ω and L = 1.5H, to make the circuit overdamped, we can solve the inequality R > 2*√(L/C) for C and find that C must be:
C < L/(R/2)^2. Substituting the given values, we have C < 1.5H / (50Ω/2)^2 which leads to C < 1.5H / (25Ω)^2 = 1.5 / 625 F = 0.0024 F or 2400 μF for an overdamped response.