Answer
The current across the ammeter is $~~\frac{1}{7}~\frac{\mathscr{E}}{R}$
Work Step by Step
We can find the equivalent resistance of $R_1 = 2.00~R$ and $R$ which are in parallel:
$\frac{1}{R_{eq}} = \frac{1}{2.00~R}+\frac{1}{R}$
$\frac{1}{R_{eq}} = \frac{1}{2.00~R}+\frac{2.00}{2.00~R}$
$R_{eq} = \frac{2.00~R}{3.00}$
We can find the equivalent resistance of the bottom resistances $R$ and $R$ which are in parallel:
$\frac{1}{R_{eq}} = \frac{1}{R}+\frac{1}{R}$
$R_{eq} = \frac{R}{2}$
We can find the equivalent resistance of the circuit:
$R_{eq} = \frac{2.00~R}{3.00}+\frac{R}{2}$
$R_{eq} = \frac{4.00~R}{6.00}+\frac{3R}{6}$
$R_{eq} = \frac{7.00~R}{6.00}$
We can find the total current in the circuit:
$i = \frac{\mathscr{E}}{R_{eq}}$
$i = \frac{\mathscr{E}}{\frac{7.00~R}{6.00}}$
$i = \frac{6.00~\mathscr{E}}{7.00~R}$
Since the potential difference across $R_1$ and the upper resistance $R$ is equal, the current in $R_1$ is $\frac{2.00~\mathscr{E}}{7.00~R}$ and the current in $R$ is $\frac{4.00~\mathscr{E}}{7.00~R}$
Since the potential difference across both bottom resistances is equal, the current is $\frac{3.00~\mathscr{E}}{7.00~R}$ in both.
Therefore, the current across the ammeter is $~~\frac{1}{7}~\frac{\mathscr{E}}{R}$
