Consider the circuit shown below.

Wires $($not shown in the figure$)$ are connected to nodes A and $B($like those shown in Fig. $4\mathrm{.}57$ in the textbook$)$ and these wires can then be connected to other devices.

a$.$ What is the Thevenin equivalent emf ${}_{eq}$ of the circuit above, i$.$e$.,$ what battery could replace it and yield the same behavior when another device is connected to the wires connected to A and B $?$

Hint: Symmetry can be used to simplify the algebra. It is correct to assume that the current through the two vertical R resistors will be the same. You can make the same assumption about the two $2$R resistors $($but with a different current than through the $R$ resistors$).$ If you don't use this symmetry you will need more equations to reach the same final result.

b$.$ What is the Thevenin equivalent resistance $R_{cq}$ of the circuit?