Question

3 resistors are connected in parallel, each with resistance between 1 and 10 Ω. What is NOT a possible value for the overall equivalent resistance of the circuit?

Answer 1

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.