Respuesta :
Answer:
Therefore,
1/3 ≤ Re ≤ 10/3 ohms
The equivalent resistance CANNOT be any value outside the boundary above
That is
Re CANNOT be greater than 10/3 ohms and CANNOT be less than 1/3 ohms, given that R1,R2,R3 are all between 1 and 10ohms.
Explanation:
For a parallel resistor arrangement.
The equivalent resistance (Re) of the three resistors is given by;
1/Re = 1/R1 + 1/R2 + 1/R3
1/Re = (R2R3 + R1R3 + R1R2)/R1R2R3
Re = R1R2R3/(R2R3 + R1R3 + R1R2)
Therefore, if R1,R2,R3 are between 1-10ohms
We need to calculate the range of values of Re.
Taking the lower bound 1
R1= R2=R3= 1ohms
Re = 1/(1+1+1)
Re = 1/3 ohms
Taking the upper bound 10 ohms
R1= R2=R3= 10 ohms
Re = 1000/(100+100+100)
Re = 1000/300
Re = 10/3 ohms
Therefore,
1/3 ≤ Re ≤ 10/3 ohms
The equivalent resistance CANNOT be any value outside the boundary above
That is
Re cannot be greater than 10/3 ohms and cannot be less than 1/3 ohms, given that R1,R2,R3 are all between 1 and 10ohms.
