A $0\mathrm{.}160$ HH inductor is connected in series with a $82$ resistor and an ac source. The voltage across the inductor is vL$=(13\mathrm{.}0$V$)$sin$[(470$rad$/$s$)$t$]$vL$=(13\mathrm{.}0$V$)$sin$[(470$rad$/$s$)$t$].$

Part A

Derive an expression for the voltage vRvR across the resistor.

Express your answer in terms of the variables LL$,$ RR$,$ VLVL $($amplitude of the voltage across the inductor$),$ $,$ and tt$.$

Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

vRvR $=$

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Part B

What is vRvR at $1\mathrm{.}93$ msms$?$

Express your answer with the appropriate units.

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vRvR $=$

nothingnothing