Question

A circular coil of radius $0.1\, m$ has $80$ turns of wire. If the magnetic field through the coil increases from $0\, to\, 2$ tesla in $0.4 \,s$ and the coil is connected to a $11 \,\Omega$ resistor, what is the current flow through the resistor during the 0.4 s?

• A. $\left( \frac{8}{7} \right) A$
• B. $\left( \frac{7}{8} \right) A$
• C. 8 A
• D. 7 A

Answer 1

Answer: (A)

$\left( \frac{8}{7} \right) A$

Answer 2

$\left|\varepsilon \right|=N \frac{d\phi}{dt} =NA \frac{dB}{dt}$
$= 80 \times\frac{22}{7} \times\left(0.1\right)^{2} \left(\frac{2.0}{0.4}\right)$
$I =\frac{\left|\varepsilon \right|}{R} =80 \times\frac{22}{7} \times\frac{\left(0.1\right)^{2 }\times5}{11}=\frac{8}{7}A$