Chapter 30: Q61P (page 900)

A coil is connected in series with a $10.0 k Ω$ resistor. An ideal 50.0 Vbattery is applied across the two devices, and the current reaches a value of 2.00 mAafter 5.00 ms.(a) Find the inductance of the coil. (b) How much energy is stored in the coil at this same moment?

Short Answer

Expert verified

a) $L = 97.9 H$

b) $U_{b} = 0.196 mJ$

Step by step solution

Given

$R = 10 k Ω = 10 \times 10^{3} Ω E = 50.0 V I = 2.00 m A = 2.00 \times 10^{- 3} A t = 5.00 m s = 5 \times 10^{- 3} s$

Understanding the concept

Here we have to use the formula for current through RL circuit to find inductance. Then by using formula for energy stored by inductor’s magnetic field, we can calculate the energy stored in the coil.

Formula:

$i = \frac{E}{R} (1 - e^{\frac{t}{{}^{t}L}}) U_{b} = 0.5 L i^{2}$

(a) Find the inductance of the coil

Here, the rise of current for RL circuit is as follows:

$i = \frac{E}{R} (1 - e^{- \frac{t}{{}^{t}L}}) i = \frac{E}{R} (1 - e^{- \frac{t \times R}{L}}) 2.00 \times 10^{- 3} = \frac{50}{10 \times 10^{3}} (1 - e^{- \frac{5 \times 10^{- 3} \times 10 \times 10^{3}}{L}}) 0.4 = (1 - e^{\frac{50}{- L}}) 0.6 = e^{- 50 / L} L = - \frac{50}{I n (0.6)} L = 97.9 H$

(b) Calculate how much energy is stored in the coil at this same moment

The inductor’s magnetic field stores energy and is given by

$U_{b} = 0.5 L i^{2} U_{b} = 0.5 \times 97.9 \times (2.00 \times 10^{- 3})^{2}$

$U_{b} = 0.196 mJ$

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A coil is connected in series with a $10.0 k Ω$ resistor. An ideal 50.0 Vbattery is applied across the two devices, and the current reaches a value of 2.00 mAafter 5.00 ms.(a) Find the inductance of the coil. (b) How much energy is stored in the coil at this same moment?

Short Answer

Step by step solution

Given

Understanding the concept

(a) Find the inductance of the coil

(b) Calculate how much energy is stored in the coil at this same moment

One App. One Place for Learning.

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A coil is connected in series with a 10.0kΩresistor. An ideal 50.0 Vbattery is applied across the two devices, and the current reaches a value of 2.00 mAafter 5.00 ms.(a) Find the inductance of the coil. (b) How much energy is stored in the coil at this same moment?

Short Answer

Step by step solution

Given

Understanding the concept

(a) Find the inductance of the coil

(b) Calculate how much energy is stored in the coil at this same moment

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Famous Physicists

Turning Points in Physics

Translational Dynamics

Modern Physics

Wave Optics

Study anywhere. Anytime. Across all devices.

A coil is connected in series with a $10.0 k Ω$ resistor. An ideal 50.0 Vbattery is applied across the two devices, and the current reaches a value of 2.00 mAafter 5.00 ms.(a) Find the inductance of the coil. (b) How much energy is stored in the coil at this same moment?