如图所示电路,R2=3Ω,R3=6Ω.当S1、S2都闭合时,电流表的示数为2A;当S1、S2都断开时,电流表的示数为0.5A. (1)求电源电压; (2)请用两种方法求出电阻R1的阻值.(设电源电压恒定不变)

问题描述:

如图所示电路,R2=3Ω,R3=6Ω.当S1、S2都闭合时,电流表的示数为2A;当S1、S2都断开时,电流表的示数为0.5A.

(1)求电源电压;
(2)请用两种方法求出电阻R1的阻值.(设电源电压恒定不变)

(1)当S1、S2都闭合时,R1被短路,R2和R3并联:

1
R23
=
1
R2
+
1
R3
1
R23
=
R2+R3
R2R3
,所以R23=
R2R3
R2+R3

电源电压:U=IR23=I
R2R3
R2+R3
=2A×
3Ω×6Ω
3Ω+6Ω
=4V

(2)当S1、S2都断开时,R1和R3串联:
解法一:串联的总电阻:R13=
U
I′
=
4V
0.5A
=8Ω,
        则R1=R13-R3=8Ω-6Ω=2Ω.
解法二:R3两端的电压:U3=I′R3=0.5A×6Ω=3V,
        R1两端的电压:U1=U-U3=4V-3V=1V,
        R1的阻值:R1=
U1
I′
=
1V
0.5A
=2Ω.
答:(1)电源电压是4V.(2)R1的阻值是2Ω.