Three resistors have resistances in the ratio 1:2:3. When they are connected in parallel, the effective resistance is 60 Ω. What is the effective resistance when they are connected in series?
Three resistors have resistances in the ratio 1:2:3. When they are connected in parallel, the effective resistance is 60 Ω. What is the effective resistance when they are connected in series?
Right Answer is:
660 Ω
SOLUTION
Let’s denote the resistances of the three resistors as R, 2R, and 3R, respectively, since they are in the ratio 1:2:3.
When connected in parallel:
The equivalent resistance (Rp) of resistors connected in parallel is given by:
1/Rp = 1/R + 1/2R + 1/3R
Given that Rp = 60 Ω, we can solve for R:
1/60 = 1/R + 1/2R + 1/3R 1/60
= (6 + 3 + 2) / 6R
1/60 = 11 / 6R
R = 110 Ω
When connected in series:
The equivalent resistance (Rs) of resistors connected in series is the sum of individual resistances:
Rs = R + 2R + 3R = 6R
Substituting the value of R:
Rs = 6 * 110 Ω = 660 Ω
Therefore, the effective resistance when the resistors are connected in series is 660 Ω.