$解:(1)U=I_1(R_1+R_L)=0.4\ \text {A}×(20Ω+R_L)①$
$U=I_2(\frac 12R_2+R_L)=0.3\ \text {A}×(\frac 12×60Ω+R_L)②$
$联立①②,解得U=12\ \text {V},R_L=10Ω$
$(2)I_{ L}=\frac {U_{L }}{R_{L }}=\frac {{ 5 }\ \text {V}}{{ 10 }Ω}={ 0.5 }\ \text {A}$
$U_2=U-U_L=12\ \text {V}-5\ \text {V}=7\ \text {V}$
$R_{ 2 }'=\frac {U_{ 2 }}{I_{ L }}=\frac {{ 7 }\ \text {V}}{{ 0.5 }\ \text {A}}={ 14 }Ω$
$(3)I_小=\frac {U}{R_1}+\frac U{R_2}=\frac {12\ \text {V}}{20Ω}+\frac {12\ \text {V}}{60Ω}=0.8\ \text {A}$
固电流表应接0~3 A量程,电流为3 A时,滑动变阻器接入阻值最小,此时
$I_2'=I_大-I_1=3\ \text {A}-0.6\ \text {A}=2.4\ \text {A}$
$R_{ 2 }''=\frac {U_{ }}{I_{ 2}'}=\frac {{ 12 }\ \text {V}}{{ 2.4 }\ \text {A}}={ 5 }Ω$
所以滑动变阻器的阻值可调范围为5~60Ω,电流表的变化范围是0.8~3 A.