The-following-diagram-shows-the-relationship-between-electromotive-force-e-m-f-and-the-time-t-in-a-dynamo-coil-During-the-time-interval-from-t-0-to-t-1-30-seconds-the-average-electromotive-f

Question Number 215410 by York12 last updated on 05/Jan/25

The following diagram shows the relationship

between electromotive force (e . m . f) and the time (t) in a dynamo

coil . During the time interval from t = 0 to t = \frac{1}{30} seconds,

the average electromotive force (e . m . f) induced in the coil is :

(a) 42.46 V

(b) 19.11 V

(c) 127.39 V

(d) 173.21 V

Commented by York12 last updated on 05/Jan/25

Commented by York12 last updated on 05/Jan/25

My idea was

emf = A B N w \sin (θ) = A B N \frac{d (θ)}{d (t)} \sin (θ)

\Rightarrow e m f d (t) = A B N \sin (θ) d (θ)

\Rightarrow \underset{t_{1}}{\int^{t_{2}}} e m f d (t) = A B N \underset{θ_{1}}{\int^{θ_{2}}} \sin (θ) d (θ) = \frac{{e m f}_{m a x}}{w} \underset{θ_{1}}{\int^{θ_{2}}} \sin (θ) d (θ)

= \frac{{e m f}_{m a x}}{w} [\cos (θ_{1}) - \cos (θ_{2})] = \frac{{e m f}_{m a x}}{w} [\cos ({w t}_{1}) - \cos ({w t}_{2})]

I do not know what is wrong with my approach,

please help .

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