解:$(1)$已知指示灯闪烁了$280$次,则消耗的电能$W=\frac {280}{1200}\mathrm {kW}· h=\frac {280}{1200}×3.6×10^6J = 8.4×10^5J。$
根据功率公式$P = \frac {W}{t},$$t = 7\mathrm {\mathrm {min}}=7×60s = 420s$
可得实际功率$P_{实}=\frac {W}{t}=\frac {8.4×10^5J}{420s}=2000W$
$ (2) $电水壶电阻$R=\frac {U_{额}^2}{P_{额}}=\frac {(220V)^2}{2420W}=20\ \mathrm {Ω}。$
再根据$P_{实}=\frac {U_{实}^2}{R},$可得$U_{实}=\sqrt {P_{实}R}=\sqrt {2000W×20\ \mathrm {Ω}}=200V。$
$ (3)$由$ρ=\frac {m}{V},$$V = 2L = 2×10^{- 3}\mathrm {m^3},$
可得水的质量$m=ρ_{水}V=1×10^3\ \mathrm {kg/m}^3×2×10^{-3}\ \mathrm {m^3}=2\ \mathrm {kg}。$
根据$Q_{吸}=c_{水}m(t - t_{0}),$$c_{水}=4.2×10^3J/(\mathrm {kg·℃}),$$t = 100℃,$$t_{0}=20℃,$
可得$Q_{吸}=4.2×10^3J/(\mathrm {kg·℃})×2\ \mathrm {kg}×(100℃ - 20℃)=6.72×10^5J。$
最后根据效率公式$\eta =\frac {Q_{吸}}{W}×100\%=\frac {6.72×10^5J}{8.4×10^5J}×100\% = 80\%。$
$ (4)$变短$ $ 变大