Question

The charge flowing through the conductor varies with time as $Q=at-b{t}^2$. Then, the current

• A. increases linearly with time
• B. reaches a minimum and then increases
• C. falls to zero after a time $t=\frac{a}{2b}$
• D. changes at the constant rate $-2b$

Answer 1

Answer: (C), (D)

falls to zero after a time $t=\frac{a}{2b}$
changes at the constant rate $-2b$

$Q=at-b{t}^2$

Current, $I=\frac{dQ}{dt}=a-2bt\Rightarrow$linearly decreases with time.

for $I=0\Rightarrow a-2bt=0,ort=\frac{a}{2b}$

Thus, current rate is $\frac{dI}{dt}=-2b$ . Its rate will be constant.

Ans: C,D