Chapter 30: Q. 74 (page 874)

74. II The inductor in FIGURE P30.74 is a $9.0 - cm$ -long, $2.0 - cm -$ diameter solenoid wrapped with 300 turns. What is the current in the circuit $10 μ s$ after the switch is moved from a to b ?

Short Answer

Expert verified

Hence, the required current is $0.093 A$

Step by step solution

Step 1. Given information

The number of turns if 300, and length of inductor is 9 cm

The radius of the coil is,

$\begin{array}{l} r = \frac{d}{2} \\ r = \frac{2 cm (\frac{1 m}{100 cm})}{2} = 0.01 m \end{array}$

Step 2. Explanation

The inductance of the coil is,

$\begin{array}{l} L = \frac{μ_{0} N^{2} A}{l} \\ L = \frac{μ_{0} N^{2} π r^{2}}{l} \\ L = \frac{(4 π \times 10^{- 7} T \cdot m / A) {(300)}^{2} π {(0.01 m)}^{2}}{9 cm (\frac{1 m}{100 cm})} \\ = 3.94 \times 10^{- 4} H \end{array}$

According to ohm's law, the initial current is,

$\begin{array}{l} I_{0} = \frac{V_{0}}{R} \\ I_{0} = \frac{6 V}{30 Ω} = 0.2 A \end{array}$

The expression for the current in the coil is,

$\begin{array}{l} I = I_{0} e^{\frac{- t}{τ}} \\ I = I_{0} e^{\frac{- t}{(\frac{L}{R})}} = I_{0} e^{\frac{- R t}{L}} \\ I = I_{0} e^{\frac{- R t}{L}} \\ I = (0.2 A) e^{- (30 Ω) (10 μ s) (\frac{10^{- 4} s}{1 / s})} \\ = 0.093 A \end{array}$

Hence, the required current is $0.093 A$

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74. II The inductor in FIGURE P30.74 is a $9.0 - cm$ -long, $2.0 - cm -$ diameter solenoid wrapped with 300 turns. What is the current in the circuit $10 μ s$ after the switch is moved from a to b ?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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74. II The inductor in FIGURE P30.74 is a 9.0−cm-long, 2.0−cm−diameter solenoid wrapped with 300 turns. What is the current in the circuit 10μsafter the switch is moved from a to b ?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electromagnetism

Rotational Dynamics

Particle Model of Matter

Wave Optics

Electric Charge Field and Potential

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

74. II The inductor in FIGURE P30.74 is a $9.0 - cm$ -long, $2.0 - cm -$ diameter solenoid wrapped with 300 turns. What is the current in the circuit $10 μ s$ after the switch is moved from a to b ?