Question

Three electric resistors are placed in circuits as shown. It is not necessary for the resistors to have the same resistance. a. In which of the various configurations shown do at least TWO resistors carry the same electric current? _____ b. In which of the various configurations shown do at least Two resistors have the same electric potential across them? c. In which of the various configurations shown do THREE resistors carry the same electric current?_____ d. In which of the various configurations shown do THREE resistors have the same electric potential (voltage) across them? _____ e. Considering now that each resistor has the same resistance R, rank from HIGH to low the combinations based on equivalent resistances. Show work!

Answer 1

a)

As current is same in series we can easily see there are three combination in which two resistor carry the same current and the combinattion are.

C,D,E

b)

As potential difference is same in parallel we can easily see there are two combination in which two resistor carry the same potential difference and the combinattion are.

A,B

c)

As current is same in series we can easily see there is only one combination in which three resistor carry the same current and the combinattion is.

C

d)

As potential difference is same in parallel we can easily see there is only one combination in which three resistor carry the same potential difference and the combinattion is.

A

e)

Now we can easilly find the equivalent resistor as,

$A=\frac{R}{3}$

$B=\frac{3R}{2}$

$C=3R$

$D=\frac{2R}{3}$

$E=\frac{2R}{3}$

So as can see from above equation we have,

$C>B>(D=E)>A$