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The number of observed giant radio sources (GRSs) has increased significantly in recent years, yet their formation mechanisms remain elusive. The discovery of giant radio galaxies within galaxy clusters has further intensified the ongoing debates. We utilize magnetohydrodynamic simulations to investigate the formation of GRSs in cluster environments. To avoid confounding the effects of power and total energy injection, we hold the energy of jet outbursts fixed and study the effect of power by varying the active duration of the jets. Furthermore, we examine the roles of magnetic, thermal, and kinetic energy components by adjusting their fractions in the jets. Additionally, we calculate radio emission for comparison with observations in the radio power-linear size diagram (P-D diagram). Finally, we also study the energy transport processes of different jets. We find the 'lower power-larger bubble' effect: lower-power jets tend to produce larger radio sources with fixed total jet energy. Regarding different energy components, jets dominated by toroidal magnetic field energy generate larger radio sources than kinetic and thermal energy-dominated jets. Conversely, strong poloidal magnetic fields hinder radio lobe growth. When injecting \(2.06 \times 10^{59}\) erg into a \(10^{14}\) solar mass halo, only jets with powers of approximately \(10^{-4}\) to \(10^{-3}\) Eddington luminosity efficiently traverse the observational region in the P-D diagram. Our findings suggest that energetic, long-lasting (low-power), continuous jets endowed with significant toroidal magnetic fields facilitate the formation of GRSs in cluster environments. However, although the jets with significantly lower power can generate substantially larger radio sources, their faintness may render them unobservable.