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Solve the given problems.The current $i$ (in $A$ ) in an amplifier circuit as a function of the time $t$ (in s) is given by $i=0.10 \cos (120 \pi t+\pi / 6) .$ The voltage caused by the changing current is given by $V_{L}=L(d i / d t),$ where $L$ is the inductance (in $\mathrm{H}$ ). Find the expression for the voltage across a $2.0-\mathrm{mH}$ inductor in the circuit.

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

03:42

An RL circuit with a $$5 -…

04:15

A 0.180-H inductor is conn…

02:57

The voltage in a circuit w…

13:12

An $L C$ scries circuit ha…

05:21

Consider a series circuit …

06:01

A resistor and inductor ar…

03:18

A $25-\mathrm{mH}$ inducto…

07:03

The output voltage of an A…

04:54

An ac circuit has a single…

04:03

A series circuit has an in…

This problem 56. We see that the current is going to be given as a function of time. So we'll have I equals zero 10 co sign of 1 20 pi T Plus. High over six. And we want to know um we want to find the expression for the voltage across 82 milla Henry in dr and we know that the voltage across the conductor is L. D. I. D. T. So in this case we take the derivative um we take the derivative across the induct. Er so that's going to end up giving us if this was um alfa backs for example. And this was X. Then we know that if it's lbgt we would take f prime of X. We take the derivative of the conductor but then we're going to multiply that times two milla Henry, so 0.2 That would end up giving us our resulting expression for the voltage.

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In mathematics, precalculus is the study of functions (as opposed to calculu…

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The voltage in a circuit with alternating current is given by$$V(t)=160 …

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