Answer
$0.050~A$
Work Step by Step
To find the potential difference $\Delta V_1$ across $R_1$, we can consider the potential difference clockwise around the loop including resistor $R_1$ and emf $\mathscr{E}_2$:
$-5.0~V+\Delta V_1 = 0$
$\Delta V_1 = 5.0~V$
We can find the current $i_1$ in $R_1$:
$i_1 = \frac{5.0~V}{100~\Omega} = 0.050~A$
