Question

The voltage across a parallel-plate capacitor with area A = 820 cm2 and separation d = 5 mm varies sinusoidally as V = (14 mV)cos(170t), where t is in seconds. Find the displacement current between the plates. (Use the following as necessary: t. Do not use other variables, substitute numeric values. Assume that Id is in amperes. Do not include units in your answer.)

Answer 1

`I_d = -3.454*10^(-10) \ \ (sin ( \ 170 \ t))`

Step-by-step explanation:

The displacement current
`I_d` is given by the expression;

`I_d = \epsilon _o (d \phi _ E )/(dt)`

where

`\phi _ E = A.E \\ \\ \\\phi _E = A. (V)/(d) \\ \\ \\\phi _E = (A)/(d)(14*10^(-3))(cos \ 170 \ t ) \\ \\ \\\phi _E = (820*10^(-4))/(5*10^(-3)) * (14*10^(-3))(cos \ 170 \ t ) \\ \\ \\\phi _E = 2296*10^(-4) (cos \ 170 \ t)`

`I_d = \epsilon _o (d \phi _ E )/(dt)`

`I_d = 8.85*10^(-12)(2296*10^(-4))(-170)(sin(170 \ t))`

`I_d = -3.454*10^(-10) \ \ (sin ( \ 170 \ t))`