A \( 25\,\mu\mathrm{F} \) capacitor, a 0.10 H inductor and a 25 \( \Omega \) resistor are connected in series with an ac source of emf \( \varepsilon = 310\sin 314t \). What is the frequency of AC source?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 50 Hz
An ac emf is written as \( \varepsilon = \varepsilon_0 \sin\omega t \), where \( \omega \) is the angular frequency. The frequency of the source is \( \nu = \omega/2\pi \). The capacitor, inductor and resistor do not change the frequency; they are extra data.
\( \varepsilon_0 = 310\,\mathrm{V} \)
\( \omega = 314\,\mathrm{rad\,s^{-1}} \)
\( \displaystyle \nu = \frac{\omega}{2\pi} = \frac{314}{2 \times 3.14} = 50\,\mathrm{Hz} \)