解:$(1)R_{ L}=\frac {U_{L }^2}{P_{ L }}=\frac {({ 6 }\ \text {V})^2}{{ 3 }\ \text {W}}={12 }Ω$
$(2)U=U_L=6\ \text {V}$
$(3)R=R_{L}=12\ \mathrm {Ω},$所以$U_L'=U_R'=3\ \text {V}$
$P_{ L }'=\frac {U_{L }'^2}{R_{ L }}=\frac {({3 }\ \text {V})^2}{{12 }Ω}={ 0.75 }\ \text {W}$