Question

The discharge of a capacitor through a ballistic galvanometer produces a damped frequency of 0.125 Hz and successive swings of 120, 96 and 76.8 mm. The logarithmic decrement is?

(a) 0.225

(b) 0.565

(c) 0.484

(d) 0.7887

I got this question during an interview for a job.

My question is based upon Advanced Problems on Indicating Instruments topic in section Extension of Instrument Ranges of Electrical Measurements

Answer 1

Correct option is (a) 0.225

To explain: Logarithmic decrement, δ = \(ln \frac{x_1}{x_2} = ln \frac{120}{96}\) = 0.225

Now, δ is related to damping ratio K as, K = \(\frac{1}{(1 + (\frac{2π}{δ})^2)^{0.5}}\)

K = \(\frac{1}{(1 + (\frac{2π}{0.225})^2)^{0.5}}\)

∴ K = 0.0357.