\(i=\frac{V}{220+R}\) .....\((i)\)
When \(\mathrm{k}_{1}\) and \(\mathrm{k}_{2}\) are closed.
\(\mathrm{KVL} \rightarrow\)
\(\left(\frac{\mathrm{iR}}{25}+\frac{\mathrm{i}}{5}\right) 220+\frac{\mathrm{i}}{5} \mathrm{R}=\mathrm{V}\)
\(\left(\frac{\mathrm{i} \mathrm{R}}{25}+\frac{\mathrm{i}}{5}\right) 220+\frac{\mathrm{i}}{5} \mathrm{R}=\mathrm{i}(220+\mathrm{R}) \quad\) From eq \((i)\)
\(\Rightarrow \quad R=22\, \Omega\)