Q. 70 70. II The current through induc... [FREE SOLUTION]

Chapter 30: Q. 70 (page 874)

70. II The current through inductance $L$ is given by $I = I_{0} e^{鈭� t / 蟿}$ .
CALC a. Find an expression for the potential difference $螖 V_{L}$ across the inductor.
b. Evaluate $螖 V_{L}$ at $t = 0, 1.0$ , and $3.0 ms$ if $L = 20 mH, I_{0} = 50 mA$ , and $蟿 = 1.0 ms$ .

Short Answer

Expert verified

Part (a) The potential difference is $螖 V_{L} = \frac{L I_{0}}{蟿} e^{鈭� \frac{t}{t}}$

Part (b) Potential difference at different times

time (S)	potential difference
0 s	1000 mV
1 s	370 mV
2 s	140 mV
3 s	50 mV

Step by step solution

Part (a)

The expression for current is,

$I = I_{0} e^{\frac{t}{r}}$

The expression for the potential difference, $螖 V_{L}$ is

$\begin{array}{l} 螖 V_{L} = 鈭� L \frac{d I}{d t} \\ 螖 V_{L} = 鈭� L \frac{d}{d t} (I_{0} e^{\frac{t}{t}}) \\ 螖 V_{L} = \frac{L I_{0}}{蟿} e^{鈭� \frac{t}{t}} 鈥� 鈥� (1) \end{array}$

The potential difference is $\frac{L I_{0}}{蟿} e^{鈭� \frac{t}{t}}$

Part (b)

$L = 20 mH$ , $蟿 = 1.0 ms$ and $I_{0} = 50 mA$

At, $t = 0 鈥娾赌� s$

$\begin{array}{l} 螖 V_{L 1} = \frac{(20 mH) (50 mA)}{(1.0 ms)} e^{鈭� 0} \\ = 1000 mV \end{array}$

At, $t = 1 鈥娾赌� s$

$螖 V_{L 2} = \frac{(20 mH) (50 mA)}{(1.0 ms)} e^{鈭� 1} = 370 mV$

At, $t = 2 鈥娾赌� s$

$螖 V_{L 3} (t = 2 s) = \frac{(20 mH) (50 mA)}{(1.0 ms)} e^{鈭� 2} = 140 mV$

At, $t = 3 鈥娾赌� s$

$螖 V_{L} = \frac{(20 mH) (50 mA)}{(1.0 ms)} e^{鈭� 3} = 50 mV$

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91影视

70. II The current through inductance $L$ is given by $I = I_{0} e^{鈭� t / 蟿}$ .
CALC a. Find an expression for the potential difference $螖 V_{L}$ across the inductor.
b. Evaluate $螖 V_{L}$ at $t = 0, 1.0$ , and $3.0 ms$ if $L = 20 mH, I_{0} = 50 mA$ , and $蟿 = 1.0 ms$ .

Short Answer

Step by step solution

Part (a)

Part (b)

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91影视

70. II The current through inductance Lis given byI=I0e鈭�t/蟿 .CALC a. Find an expression for the potential difference 螖VLacross the inductor.b. Evaluate 螖VLat t=0,1.0, and 3.0msif L=20mH,I0=50mA, and 蟿=1.0ms.

Short Answer

Step by step solution

Part (a)

Part (b)

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Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Translational Dynamics

Work Energy and Power

Conservation of Energy and Momentum

Linear Momentum

Space Physics

Force

Study anywhere. Anytime. Across all devices.

70. II The current through inductance $L$ is given by $I = I_{0} e^{鈭� t / 蟿}$ .
CALC a. Find an expression for the potential difference $螖 V_{L}$ across the inductor.
b. Evaluate $螖 V_{L}$ at $t = 0, 1.0$ , and $3.0 ms$ if $L = 20 mH, I_{0} = 50 mA$ , and $蟿 = 1.0 ms$ .