So, \(\mathrm{V}_{\mathrm{AB}}=\mathrm{i}_1 \times 20 \Omega=20 \times 0.3 \mathrm{~V}=6 \mathrm{~V}\)

\( \mathrm{i}_2=\frac{6 \mathrm{~V}}{15 \Omega}=\frac{2}{5} \mathrm{~A} \)

\( \mathrm{i}_1+\mathrm{i}_2+\mathrm{i}_3=\frac{9}{10} \mathrm{~A} \)

\( \frac{3}{10}+\frac{2}{5}+\mathrm{i}_3=\frac{9}{10} \)

\( \frac{7}{10}+\mathrm{i}_3=\frac{9}{10} \)

\( \mathrm{i}_3=0.2 \mathrm{~A} \)

\( \text { So, } \mathrm{i}_3 \times \mathrm{R}_1=6 \mathrm{~V} \)

\( (0.2) \mathrm{R}_1=6 \)

\( \mathrm{R}_1=\frac{6}{0.2}=30 \Omega\)