An ideal ac generator supplies an emf that varies with time according to

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

\varepsilon=\varepsilon_0\,\sin\!\left(\omega t\right)

, where the frequency is

50\,\text{Hz}

. (i) Starting from this relation, derive an expression for the time

t_k

taken for the emf to reach a value

k\,\varepsilon_0

(

0<k<1

) for the first time after a zero crossing. (ii) Using your expression, calculate

t_{0.8}

, the time required for the emf to reach

0.80\,\varepsilon_0

. (iii) During the interval found in part (ii), through what angle (in degrees) has the generator coil rotated?