Question

The normal magnetic flux passing through a coil changes with time according to the equation $\phi = 6t^2 - 5t + 1$. What is the magnitude of the induced current at $t = 0.253\, s$ and resistance $10 \, \Omega$ ?

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

Answer 1

Answer: (D)

0.2 A

Answer 2

Here ,
Magnetic flux, $\phi = 6t^2 - 5t + 1$
Resistance, $R = 10\, \Omega$
The induced emf is
$\varepsilon = - \frac{d\phi}{dt} = - \frac{d}{dt} \left(6t^{2} - 5t+ 1\right)=-\left(12t - 5 \right)$
At $t = 0.253 \,s$
$\varepsilon = -(12 \times 0.253 - 5 ) = 1.964 \, V = 2 V$
$\therefore$ Induced current, $I = \frac{ \varepsilon}{R} = \frac{2}{10} = 0.2 A$