$9\mathrm{.}182.$ In the eircuit shown in Fig. $3\mathrm{.}45$ the sources have emf

$81=15$ V$,82=20$ V$,8,=2\mathrm{.}5$ V$,$ and the resistances ar

equal to R$1=108,$ Rg $=20$Q$,$ R$,=30$Q$.$ The internal resistance

of the sources are

negligible. Find:

$($a$)$ the current flowing through the resistance R$1$:

$($b$)$ a potential difference a $-4$

between the points A and B$.$

$3\mathrm{.}183.$ Find the current flowing through the resistance Rin the circuit shown in Fig. $3\mathrm{.}46.$ The internal resistances of the