# The voltage V induced in an inductor in an electric circuit is given by the equation below where...

## Question:

The voltage {eq}V {/eq} induced in an inductor in an electric circuit is given by the equation below where {eq}L {/eq} is the inductance (in {eq}H {/eq}). Find the expression for the voltage induced in a {eq}1.69\ H {/eq} inductor if {eq}\displaystyle q = \sqrt {2t + 5} - 5.\\ V = L {d^2 q \over dt^2} {/eq}

## Double derivatives

{eq}\displaystyle \frac{dx^n}{dx}=n(x^{n-1}) {/eq}

The voltage induced is always equal to inductance times the rate of change of current.

rate of change of current is equal to double derivative of rate of change of charge.

## Answer and Explanation: 1

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Given

{eq}\displaystyle q = \sqrt {2t + 5} - 5.\\ V = L {d^2 q \over dt^2} {/eq}

{eq}\displaystyle...

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