$I\ =\ \frac{\ VB}{R+r}$I =  VBR+r​​

$\ \frac{1}{2}=\frac{VB}{2+r}\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(1\right)$ 12​=VB2+r​∴                 (1)​

$\ \frac{1}{6}=\frac{VB}{7.8+r}\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(2\right)$ 16​=VB7.8+r​∴                 (2)​

بقسمة (1) .(2)

$\ 3=\frac{7.8+r}{2+r}$ 3=7.8+r2+r​​

6+3r=7.8+r 1.8=2r

r=0.9$\Omega$Ω​

بالتعويض فى (1) :

$\frac{1}{2}=\frac{VB}{2+0.9}\therefore$12​=VB2+0.9​∴​

$\therefore$∴​2VB=2.9 VB=1.45V