Chapter 30: Q80P (page 901)

In Fig. 30-63, $R = 4.0 kΩ$ , $L = 8.0 μH$ and the ideal battery has $ε = 20 v$ . How long after switch S is closed is the current 2.0 mA?

Short Answer

Expert verified

For $1.0 \times 10^{- 9} s$ after switch S is closed, the value for the current is 2.0 mA

Step by step solution

Given

$R = 4.0 kΩ = 4.0 \times 10^{3} Ω L = 8.0 μH = 8.0 \times 10^{- 6} H ε = 20 v I = 2.0 mA = 2.0 \times 10^{- 3} A$

Understanding the concept

We have the equation for current in the loop. We rearrange the equation to find the required value.

Formula:

$I = \frac{ε}{R} (1 - e^{- \frac{t}{τ_{L}}})$

$τ_{L} = \frac{L}{R}$

Calculate how long after switch S is closed is the current 2.0 mA

We have,

$I = \frac{ε}{R} (1 - e^{- \frac{t}{τ_{L}}})$

But,

$τ_{L} = \frac{L}{R} τ_{L} = \frac{8.0 \times 10^{- 6}}{4.0 \times 10^{3}} τ_{L} = 2.0 \times 10^{- 9} s 2.0 \times 10^{3} = \frac{20}{4.0 \times 10^{3}} \times (1 - e^{\frac{- t}{2.0 \times 10^{- 9}}}) (1 - e^{\frac{- t}{2.0 \times 10^{- 9}}}) = \frac{2.0 \times 10^{- 3} \times 4.0 \times 10^{3}}{20} (1 - e^{\frac{- t}{2.0 \times 10^{- 9}}}) = 0.4 e^{\frac{- t}{2.0 \times 10^{- 9}}} = 0.4 - 1 e^{\frac{- t}{2.0 \times 10^{- 9}}} = - 0.6 e^{\frac{- t}{2.0 \times 10^{- 9}}} = 0.6$

Taking natural log at both the sides, we get

$- \frac{t}{2.0 \times 10^{- 9}} = In (0.6) \frac{t}{2.0 \times 10^{- 9}} = 0.51 t = 2.0 \times 10^{- 9} \times 0.51 t = 1.0 \times 10^{- 9} s$

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In Fig. 30-63, $R = 4.0 kΩ$ , $L = 8.0 μH$ and the ideal battery has $ε = 20 v$ . How long after switch S is closed is the current 2.0 mA?

Short Answer

Step by step solution

Given

Understanding the concept

Calculate how long after switch S is closed is the current 2.0 mA

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In Fig. 30-63, R=4.0kΩ,L=8.0μHand the ideal battery hasε=20v. How long after switch S is closed is the current 2.0 mA?

Short Answer

Step by step solution

Given

Understanding the concept

Calculate how long after switch S is closed is the current 2.0 mA

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Rotational Dynamics

Engineering Physics

Physics of Motion

Space Physics

Magnetism

Study anywhere. Anytime. Across all devices.

In Fig. 30-63, $R = 4.0 kΩ$ , $L = 8.0 μH$ and the ideal battery has $ε = 20 v$ . How long after switch S is closed is the current 2.0 mA?