First slide

Maxwell's displacement current

Question

A parallel plate condenser of capacity $10 μ F$ is connected to an AC supply Voltage $e = 4 \sin (100 π t)$ . The maximum displacement current is

Moderate

A

$4 π μ A$
B

$2.8 π μ A$
C

$4 π m A$
D

$2.8 π m A$

Solution

Displacement current=conduction current
$e = e_{0} \sin (ω t)$ standard equation
$e = 4 \sin (100 π t)$ given equation
On comparing the above equations we get
$e_{0} = 4 V o l t & ω = 100 π r a d / s$
Now, we know that,
$I_{D} = \frac{e_{0}}{X_{C}}$ where $X_{C} = \frac{1}{ω C}$
$\Rightarrow I_{D} = \frac{e_{0}}{1 / ω C} = e_{0} \times ω C$
$I_{D} = 4 \times 100 π \times 10 \times 10^{- 6} A$
$I_{D} = 4 π \times 10^{- 3} A = 4 π m A$

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