Question

The magnetic flux linked with coil, in weber is given by the equation, $\phi = 5 t ^ { 2 } + 3 t + 16$ . The induced emf in the coil in the fourth second is

• A. 10 V
• B. 30 V
• C. 45 V
• D. 90 V

Answer 1

$| e | = \frac { d \phi } { d t } = \frac { d } { d t } \left( 5 t ^ { 2 } + 3 t + 16 \right) = ( 10 t + 3 )$

When $t = 3 \mathrm { sec } , e _ { 3 } = ( 10 \times 3 + 3 ) = 33 \mathrm {~V}$

When $t = 4 \mathrm { sec } , e _ { 4 } = ( 10 \times 4 + 3 ) = 43 \mathrm {~V}$

Hence emf induced in fourth second

$= e _ { 4 } - e _ { 3 } = 43 - 33 = 10 \mathrm {~V}$