[Sarah_Marie]

Resistors are components found on most circuit boards and in most electronic devices. Since resistors do not come in every size, they have to be arranged in various ways to get the needed resistance. When three resistors are in parallel, then the total resistance, Rt, can be calculated using the equation 1/Rt = 1/R1 + 1/R2 + 1/R3, where each of the resistances is in ohms.
a) Determine an expression for the total resistance, Rt.
b) Determine an expression for the total resistance of R1 = R2 = R3.
c) Determine an expression for the total resistance if R1 = 2R2 = 6R3

[Dcalderon]

1/Rt = 1/R1 + 1/R2 + 1/R3
so now answer to first question is
1/Rt=1/R1R2R3(R2R3+R1R3+R1R2)
Rt=R1R2R3/(R2R3+R1R3+R1R2)... 1

for second
just put R1 = R2 = R3=R(let) in the above equation

Rt=(R^3)/(3R^2)
Rt=R/3

for third put R1 = 2R2 = 6R3 in 1