Chapter 32: Q13P (page 967)

At what rate must the potential difference between the plates of a parallel-plate capacitor with a $2.0 μ F$ capacitance be changed to produce a displacement current of $1.5 A$ ?

Short Answer

Expert verified

The rate of potential is $7.5 \times 10^{5} V/s$ .

Step by step solution

Given data

$C = 2.0 μ F$

$i_{d} = 1.5 A$

Determining the concept

By using the concept of displacement current and by using equation 32-10, write the equation for flux as a function of potential, and from that, find the rate of change of potential difference. The rate of change of potential difference across the plates of the capacitor is displacement current per unit capacitance.

Formulae are as follows:

$i_{d} = ε_{0} \frac{d ϕ_{E}}{d t}$

where, 'i' is current, $ϕ$ is the flux.

Determining the rate of change of potential difference

From the equation 32-10,

$i_{d} = ε_{0} \frac{d ϕ_{E}}{d t}$

Where, $ϕ = A E$ theand the $E = \frac{V}{d}$ .

So,

$ϕ_{E} = \frac{A V}{d}$

So,

$i_{d} = \frac{A ε_{0}}{d} \frac{d V}{d t}$

Where, the capacitance,

$C = \frac{A ε_{0}}{d}$

So, the rate of potential is,

$\frac{d V}{d t} = \frac{i_{d}}{C} \frac{d V}{d t} = \frac{1.5}{2.0 \times 10^{- 6}} \frac{d V}{d t} = 7.5 \times 10^{5} V/s$

Hence, the rate of potential is $7.5 \times 10^{5} V / s$ .

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At what rate must the potential difference between the plates of a parallel-plate capacitor with a $2.0 μ F$ capacitance be changed to produce a displacement current of $1.5 A$ ?

Short Answer

Step by step solution

Given data

Determining the concept

Determining the rate of change of potential difference

One App. One Place for Learning.

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At what rate must the potential difference between the plates of a parallel-plate capacitor with a2.0μF capacitance be changed to produce a displacement current of1.5A?

Short Answer

Step by step solution

Given data

Determining the concept

Determining the rate of change of potential difference

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Magnetism and Electromagnetic Induction

Electrostatics

Fields in Physics

Electromagnetism

Engineering Physics

Study anywhere. Anytime. Across all devices.

At what rate must the potential difference between the plates of a parallel-plate capacitor with a $2.0 μ F$ capacitance be changed to produce a displacement current of $1.5 A$ ?