Question

Flux φ (in weber) in a closed circuit of resistance 10 ohm varies with time t (in sec) according to the equation

$\phi = 6 t ^ { 2 } - 5 t + 1$. What is the magnitude of the induced current at t = 0.25 s?

• A. 1.2 A
• B. 0.8 A
• C. 0.6 S
• D. 0.2 A

Answer 1

Answer: (D)

0.2 A

Answer 2

By using $i = \frac { e } { R } = - \frac { 1 } { R } \frac { d \phi } { d t }$;

$i = - \frac { 1 } { 10 } \frac { d } { d t } \left( 6 t ^ { 2 } - 5 t + 1 \right) = - \frac { 1 } { 10 } ( 12 t - 5 )$;

$i = - \frac { 1 } { 10 } ( 12 \times 0.25 - 5 ) = 0.2 \mathrm {~A}$