The charge flowing in a conductor varies with time as Q = at -bt^… - Vidyadip

MCQ

The charge flowing in a conductor varies with time as $Q = at -bt^2$. Then for current, which statement is incorrect.
$(A)$ decreases linearly with time
$(B)$ reaches a maximum and then decreases
$(C)$ fall to zero after time $t = a/2b$
$(D)$ changes at a rate $-2b$
Options :

A
$A, B, C$
B
$A, C, D$
C
$B, C$
✓
Only $B$

✓

Answer

Correct option: D.

Only $B$

d
$(i)$ $\mathrm{I}=\frac{\text { da }}{\mathrm{dt}}=\mathrm{a}-2 \mathrm{bt}$ (linearly decreasing with time)

$(ii)$ $\mathrm{t} \uparrow \mathrm{I} \downarrow$

$(iii)$ For $\mathrm{I}=0 ; \mathrm{a}-2 \mathrm{bt}=0 ; \mathrm{t}=\mathrm{a} / 2 \mathrm{b}$

$(iv)$ $\frac{\mathrm{dI}}{\mathrm{dt}}=-2 \mathrm{b}$

Hence option $(4)$ is incorrect.

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