First slide

Displacement current

Question

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

Moderate

A

4 $π$ mA
B

4 $π$ $μ$ A
C

2.8 $π$ mA
D

2.8 $π$ $μ$ A

Solution

Displacement current
$\begin{array}{rcl} i_{d} & = & \in_{0} \frac{dϕ}{dt} \\ = & C \frac{dV}{dt} \\ = & C \frac{d}{dt} (4 \sin 100 πt) \\ = & C x 4 x 100 π \cos (100 πt) \\ = & 400 πC \cos (100 πt) \\ i_{d} & = & i_{0} \cos (100 πt); \\ ∴ i_{0} & = & 400 πC \\ = & 400 π x 10 x 10^{- 6} \\ = & 4 π mA \end{array}$

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