(a) Define the root–mean–square (rms) value of an alternating emf. (b) For a coil of…

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

Problem

(a) Define the root–mean–square (rms) value of an alternating emf. (b) For a coil of

N

turns and area

A

rotating with uniform angular speed

\omega

in a uniform magnetic field

B

, the instantaneous emf is sinusoidal. Starting from the general expression of instantaneous emf

\varepsilon(t)

, derive the relation between its peak value

\varepsilon_0

and its rms value

\varepsilon_{\text{rms}}

. (c) Explain, with one quantitative argument, why domestic ac supply ratings (for example,

230\,\text{V}

) are always quoted in rms values rather than peak values.