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In the given circuit the switch is closed at t = 0, and the ammeter current versus time follows the displayed graph (a critically/over-damped LCR transient). With C = 4 microfarad and L = 0.1 mH, the condition shown corresponds to critical damping. Find the value of R (in ohm).

1. 10 ohm
2. 5 ohm
3. 20 ohm
4. 2.5 ohm

Correct answer: 10 ohm

Solution

Critical damping in a series LCR circuit occurs when R = 2*sqrt(L/C). The graph (no oscillation, fastest non-overshoot decay) indicates critical damping, so substituting the given L and C yields R. (The graph's qualitative shape is reconstructed to allow a self-consistent numeric answer.)

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