#### Answer

(a) $R = 54~\Omega$
(b) The current flows through the resistor from left to right.

#### Work Step by Step

(a) We can find the resistance:
$V = I~R$
$R = \frac{V}{I}$
$R = \frac{4.50~V}{83\times 10^{-3}~A}$
$R = 54~\Omega$
(b) The current flows through the circuit from points of higher potential to points of lower potential. Thus, the current flows from the positive side of the battery, around the circuit, and reaches the negative side of the battery. Therefore, the current flows through the resistor from left to right.