Q. 33 The switch in FIGURE EX30.33 has... [FREE SOLUTION]

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 $0.24 脳 10^{- 4}$ A and at $4.96 脳 10^{- 4}$ 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 :

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

$I = 0.24 脳 10^{- 4}$ A

Part (b) Step 1.

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

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

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

$t = \frac{2 脳蟺脳 \sqrt{L C}}{4}$

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 :

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

$t = 4.96 脳 10^{- 4}$ s

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91影视

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.

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