Question

31.2 damped oscillations in an rlc circuit
the slow exponential decay over many cycles of the charge on the plates of a capacitor in an rlc circuit might be due to
o a large capacitance.
o a small inductance.
o a large resistance.
o a small resistance.
o a small capacitance.

Explanation:

In an RLC circuit, the charge on the capacitor plates undergoes damped oscillations. The damping factor is related to the resistance \(R\). A smaller resistance means less energy dissipation per cycle. When the resistance is small, the exponential decay of the charge over many cycles is slow. A large capacitance or inductance affects the oscillation frequency (\(f = \frac{1}{2\pi\sqrt{LC}}\)) but not the rate of exponential decay. A large resistance would cause more energy loss per cycle and a faster decay.

Answer:

a small resistance.