Question

4. Assume you have 3 resistors with the resistances 1 Ω, 3 Ω and 7 Ω, respectively. a) How many resistors can you make from these resistors! b) Calculate the resistances of all possible resistors. 5. (FPext-ed8: 27-39) In Figure 3, E-12.0 V, R1-2000 Ω, R2 = 3000 Ω and R3-4000 Ω. What

Answer 1

Please note :-

Two resistors in series Equivalent Resistance(Req) = R1 + R2 .................... (1)

Two resistors in parallel Equivalent Resistance(Req) = 1/R1 + 1/R2 = R1R2/(R1+R2) ..............(2)

Given :-

R1 = 1 Ω

R2 = 3 Ω

R3 = 7 Ω

Different combinations possible as below :-

1.) Put R1,R2 & R3 in series.

2.) Put R1,R2 & R3 in parallel.

3.) [R1,R2 in series] parallel with R3

4.) [R2,R3 in series] parallel with R1

5.) [R3,R1 in series] parallel with R2

6.) [R1,R2 in parallel] series with R3

7.) [R2,R3 in parallel] series with R1

8.) [R3,R1 in parallel] series with R2

Therefore you can make 8 resistors.

Part b.)

Now lets calculate the Equivalent Resistance of each combination using the formulae (1) & (2) for Req in series and parallel.

1.) Equivalent Resistance = R1 + R2 + R3 = 11 Ω

2.) Equivalent Resistance = 1/R1 + 1/R2 + 1/R3 = 21/31 Ω

3.) Equivalent Resistance = 28/11 Ω = 2.54 Ω

4.) Equivalent Resistance = 10/11 Ω = 0.9 Ω

5.) Equivalent Resistance = 24/11 Ω = 2.18 Ω

6.) Equivalent Resistance = 31/4 Ω = 7.75 Ω

7.) Equivalent Resistance = 31/10 Ω = 3.1 Ω

8.) Equivalent Resistance = 31/8 Ω = 3.875 Ω