When the switch in the figure is open the voltmeter reads $3\mathrm{.}14$ V $.$ When the switch is closed the voltmeter reads $2\mathrm{.}93$ V $,$ and the ammeter reads $1\mathrm{.}67$ A $.$

Find: $($a$)$ emf $$ of the battery.

$($b$)$ The internal resistance of the battery $r.$

$($C$)$ The resistance of $R.$

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