Question

The current through a wire varies with time as $I=I_0+Kt$, where $I_0=10$ $A$ and $K=4$ $A/s$. What is the charge that flows across a section of the wire in $10$ seconds?

• A. $10$ $C$
• B. $300$ $C$
• C. $30$ $C$
• D. $40$ $C$

Answer 1

Answer: (B)

$300$ $C$

The current through the wire varies with time as

$I=I_0+Kt$, where $I_0=10A,K=4A/s$

$t=10sec$

Charge flown $Q={\int }_0^{10}I.dt$

$Q={\int }_0^{10}(I_0+Kt)dt$

$Q=|I_{0}t+\frac{K{t}^2}{2}{|}_0^{10}$

$Q=(10\times 10+\frac{4\times 10\times 10}{2})-(10\times 0+\frac{4\times 0\times 0}{2})$

$Q=100+200=300C$

The correct option is B.