Question

The magnetic flux linked with a coil at any instant ‘t’ is given by ∅=5t³-100t+300, the e.m.f. induced in the coil at t = 2 second is(a) – 40 V(b) 40 V(c) 140 V(d) 300 V

Answer 1

answer : option (b) 40V

explanation : Then magnetic flux linked with a coil at any instant 't' is given by, $\phi=5t^3-100t+300$

we know, induced emf is the negative of rate of change of magnetic flux with respect to time.

e.g., $\xi_{in}=-\frac{d\phi}{dt}$

so, differentiate $\phi=5t^3-100t+300$ with respect to time,

so, $\frac{d\phi}{dt}=15t^2-100$

at t = 2 sec, change in magnetic flux , $\frac{d\phi}{dt}$ = 15 × (2)² - 100 = 60 - 100 = -40

now, induced emf = -(-40) = 40V

hence, option (b) is correct choice.