Question

The magnetic flux linked with a coil is given by $\varphi \left(t\right)=(2t^2+3t+1)\text{Wb}.$ The charge that flows through the coil in time duration $t=1\text{s}$ to $t=4\text{s}$ will be (the resistance of the coil is equal to $4\Omega$)

$[$0.77 Mark$]$

• A. $11.24\text{C}$
• B. $9.75\text{C}$
• C. $6.12\text{C}$
• D. $8.88\text{C}$

Answer 1

The correct option is B $9.75\text{C}$

Charge flown through the coil,

$=\Delta Q=\left|\frac{\Delta \varphi }{R}\right|$

$=\frac{\varphi (t=4\text{s})-\varphi (t=1\text{s})}{R}$

$=\frac{\left(\right(2\times 4^2)+(3\times 4)+1)-\left(\right(2\times 1^2)+(3\times 1)+1)}{4}$

$=\frac{(2\times 16)+12-2-3}{4}$

$=\frac{32+12-5}{4}=\frac{39}{4}=9.75\text{C}$