Question

The magnetic flux through a coil perpendicular to the plane is varying according to the relation $\phi =(5t^3+4t^2+2t-5)$ wb. Calculate the induced current through the coil at $t=2sec$, if the resistance of the coil is $5\Omega$.

Answer 1

$\varphi =(5t^3+4t^2+2t-5)$ Weber

time $t=2sec$

Resistance $=5\Omega$

induced emf $E=\frac{d\varphi }{dt}$

$\frac{d\varphi }{dt}=15t^2+8t+2$

at $t=2sec,\frac{d\varphi }{dt}=15\times 4+8\times 2+2$

$=78V$

Also $E=IR$

$E=78V,R=5\Omega$

$I=\frac{k}{R}=\frac{78}{5}=15.6A$