解:$ (1)$发电机;电磁感应
$(2)G=25\ \mathrm {kg}×10\ \mathrm {N/kg} = 250N$
重力做的功$W_{G}=Gh,$$h = 2.4m,$所以$W_{G}=250N×2.4m = 600J$
时间$t = 4\mathrm {\mathrm {min}}=4×60s = 240s$
重力做功的功率$P=\frac {W_{G}}{t}=\frac {600J}{240s}=2.5W$
$(3)$灯泡正常发光,$P_{灯}=1W,$$t = 240s$
灯泡消耗的电能$W_{电}=P_{灯}t=1W×240s = 240J$
能量转化效率$\eta =\frac {W_{电}}{W_{G}}×100\%=\frac {240J}{600J}×100\% = 40\%$
$(4)① $考虑电压表量程,$U_{1}≤3V,$根据串联电路电压特点$U = U_{0}+U_{1},$则$U_{0}=U - U_{1},$$I=\frac {U_{0}}{R_{0}}=\frac {U - U_{1}}{R_{0}},$又$I=\frac {U_{1}}{R_{1}},$所以$\frac {U - U_{1}}{R_{0}}=\frac {U_{1}}{R_{1}}。$
当$U_{1}=3V $时,$U_{0}=U - U_{1}=3.6V - 3V = 0.6V,$$I=\frac {U_{0}}{R_{0}}=\frac {0.6V}{5\ \mathrm {Ω}}=0.12A,$$R_{1}=\frac {U_{1}}{I}=\frac {3V}{0.12A}=25\ \mathrm {Ω}。$
$② $考虑$R_{0}$的电流$I_{0}≤0.3A,$根据$I=\frac {U}{R_{0}+R_{1}},$当$I = 0.3A$时,$R_{总}=\frac {U}{I}=\frac {3.6V}{0.3A}=12\ \mathrm {Ω},$$R_{1}=R_{总}-R_{0}=12\ \mathrm {Ω}- 5\ \mathrm {Ω}= 7\ \mathrm {Ω}。$
所以滑动变阻器接入电路的阻值变化范围是$7\ \mathrm {Ω}≤ R_{1}≤25\ \mathrm {Ω}。$
综上,$(2)$重力做功的功率为$2.5W;$$(3)$能量转化效率为$40\%;$$(4)$滑动变阻器接入电路的阻值变化范围是$7\ \mathrm {Ω}≤ R_{1}≤25\ \mathrm {Ω}。$