Chapter 30: Q. 70 (page 874)

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

Short Answer

Expert verified

Part (a) The potential difference is $Δ V_{L} = \frac{L I_{0}}{τ} e^{- \frac{t}{t}}$

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, $Δ V_{L}$ is

$\begin{array}{l} Δ V_{L} = - L \frac{d I}{d t} \\ Δ V_{L} = - L \frac{d}{d t} (I_{0} e^{\frac{t}{t}}) \\ Δ V_{L} = \frac{L I_{0}}{τ} e^{- \frac{t}{t}} \dots \dots (1) \end{array}$

The potential difference is $\frac{L I_{0}}{τ} e^{- \frac{t}{t}}$

Part (b)

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

At, $t = 0 s$

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

At, $t = 1 s$

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

At, $t = 2 s$

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

At, $t = 3 s$

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

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

Short Answer

Step by step solution

Part (a)

Part (b)

One App. One Place for Learning.

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70. II The current through inductance Lis given byI=I0e−t/τ .CALC a. Find an expression for the potential difference ΔVLacross the inductor.b. Evaluate ΔVLat t=0,1.0, and 3.0msif L=20mH,I0=50mA, and τ=1.0ms.

Short Answer

Step by step solution

Part (a)

Part (b)

One App. One Place for Learning.

Most popular questions from this chapter

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