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

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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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