The resistance of the filament

\(\displaystyle{R}=\frac{{V}^{{{2}}}}{{P}}\)

\(\displaystyle{R}_{{{1}}}=\frac{{120}^{{{2}}}}{{50}}={288}\ {o}{h}{m}{s}\)

\(\displaystyle{R}_{{{2}}}=\frac{{120}^{{{2}}}}{{100}}={144}\ {o}{h}{m}{s}\)

\(\displaystyle{R}_{{{3}}}=\frac{{120}^{{{2}}}}{{150}}={96}\ {o}{h}{m}{s}\)

If the filaments are conected in parallel then

\(\displaystyle{R}_{{{1}}}={R}_{{{a}}}+{R}_{{{b}}}\)

\(\displaystyle{R}_{{{a}}}={R}_{{{b}}}={144}\ {o}{h}{m}{s}\)

\(\displaystyle{R}=\frac{{V}^{{{2}}}}{{P}}\)

\(\displaystyle{R}_{{{1}}}=\frac{{120}^{{{2}}}}{{50}}={288}\ {o}{h}{m}{s}\)

\(\displaystyle{R}_{{{2}}}=\frac{{120}^{{{2}}}}{{100}}={144}\ {o}{h}{m}{s}\)

\(\displaystyle{R}_{{{3}}}=\frac{{120}^{{{2}}}}{{150}}={96}\ {o}{h}{m}{s}\)

If the filaments are conected in parallel then

\(\displaystyle{R}_{{{1}}}={R}_{{{a}}}+{R}_{{{b}}}\)

\(\displaystyle{R}_{{{a}}}={R}_{{{b}}}={144}\ {o}{h}{m}{s}\)