A circuit element is placed in a closed box. At time t=0, constan… - Vidyadip

MCQ

$A$ circuit element is placed in a closed box. At time $t=0$, constant current generator supplying a current of $1\, amp$, is connected across the box. Potential difference across the box varies according to graph shown in figure. The element in the box is :

A
resistance of $2\Omega$
B
battery of $emf\, 6V$
C
inductance of $2H$
✓
capacitance of $0.5F$

✓

Answer

Correct option: D.

capacitance of $0.5F$

d
$q=C V \Rightarrow V=\frac{1}{C} q$

$\frac{d V}{d t}=\frac{1}{C} \frac{d q}{d t}$

$\int d V=\frac{i}{C} \int d t \Rightarrow V=\frac{i}{C} t+K$

$8=\frac{1}{C} \times 3+2 \Rightarrow C=0.5 F$

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