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.

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