(2010? Fengtai District, the second model) a science and technology group of students designed and produced a multi-position electric heater model, in order to analyze the resistance of the access cir

(2010? Fengtai District, the second model) a science and technology group of students designed and produced a multi-position electric heater model, in order to analyze the resistance of the access circuit on the electric heat (1) only close S1, R1 and R2 series, equivalent circuit diagram shown in Figure 1; only close S2, R2 and R3 series, equivalent circuit diagram shown in Figure 2.

∵ P=I2R, and P3:P3′=4:1,

∴

P3

P′3

=

I21R3

I22R3

=(

I1

I2

)2=

4

1

,

Solve:

I1

I2

=

2

1

,

∵ I=

< td style="border-bottom:1px solid black">U

R

, and U1:U2=1:2,

∴

U1

U2

=

I1R1

I2R2

=

I1

I2

×< tr>

R1

R2

=< tr>

2

1

×

R1

R2

=

1

2

,

Solve:

R1

R2

=

1
	4

;

(2) ∵ the voltage of the power supply is constant,

∴

I1

I2

=

R2+R3

R1+R3

=

4R1+R3

R1+R3

=

2

1

,

Solve: R3=2R1, R2=2R3

Figure 2: I2=

U

U

R2+R3

=< /tr>

U

R2+ 1 2 R2

=

2U

3R2

,

P2=I22R2=(

2U

3R2

)2×R2=

4

4

9

×

U2

R1

+

U2

R2

=< tr>

U2

1 4 R2

+

U2

R2

=5×=5×3.6W=18W.

Answer: (1) The ratio of resistor R1 to resistor R2 is 1:4;

(2) The circuit consumes the maximum total power, which is up to 18 W.

.

U2

R2

R2