Chapter 30: Q. 33 (page 871)

The switch in FIGURE EX30.33 has been in position 1 for a long time. It is changed to position 2 at t = 0 s. a. What is the maximum current through the inductor? b. What is the first time at which the current is maximum?

Short Answer

Expert verified

The maximum current through inductor is $0.24 \times 10^{- 4}$ A and at $4.96 \times 10^{- 4}$ s current was maximum for first time.

Step by step solution

Given information

We have given that, the switch in FIGURE EX30.33 has been in position 1 for a long time. It is changed to position 2 at t = 0 s.

Part (a) Step 1.

The formula to calculate the maximum current :

$\frac{1}{2} C V^{2} = \frac{1}{2} L I^{2}$

$I = \sqrt{\frac{C V^{2}}{L}}$

Here, I = Current

C = Capacitance

V = Potential difference

L = Inductance

Step 2.

Substituting the values in the formula :

$I = \sqrt{\frac{(2 \times 10^{- 6} F) \times {(12 V)}^{2}}{50 \times 10^{- 3} H}}$

$I = 0.24 \times 10^{- 4}$ A

Part (b) Step 1.

We know that $T = \frac{2 π}{ω}$ ,and $ω^{2} = \frac{1}{L C}$

So, the first time at which the current is maximum :

$t = \frac{T}{4}$

$t = \frac{2 \times π \times \sqrt{L C}}{4}$

Here, t = Time at which current was maximum for the first time

L = Inductance

C = Capacitance

Step 2.

Substituting the values in the formula of t :

$t = \frac{2 \times 3.14 \times \sqrt{(50 \times 10^{- 3} H) \times (2 \times 10^{- 6} F)}}{4}$

$t = 4.96 \times 10^{- 4}$ s

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

The switch in FIGURE EX30.33 has been in position 1 for a long time. It is changed to position 2 at t = 0 s. a. What is the maximum current through the inductor? b. What is the first time at which the current is maximum?

Short Answer

Step by step solution

Given information

Part (a) Step 1.

Step 2.

Part (b) Step 1.

Step 2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Further Mechanics and Thermal Physics

Particle Model of Matter

Scientific Method Physics

Oscillations

Conservation of Energy and Momentum

Study anywhere. Anytime. Across all devices.