Question

Two resistor are connrcted in series given an equivalent resistance of 10ohm. When connected in parallel, gives 2.4ohm. Then the indivisual resistance are:
(A.) Each of 5ohm.
(B.) 6ohm and 4ohm.
(C.) 7ohm and 4ohm.
(D.) 8ohm and 2ohm. ​

Answer 1

Answer:

Let's start with assuming two resistances R1 and R2 respectively.

R1 + R2 = 10

As when two resistances are in series the effective resistance is the sum of the two resistances.

1/R1 + 1/R2 = 1/2.4

As when two resistances are in parallel the effective resistance is calculated as given above.

Now we rearrange the above equation.

(R1 × R2)/(R1 + R2) = 2.4

(R1 × R2) = 2.4 × (R1 + R2)

(R1 × R2) = 2.4 × 10 (From the first equation)

(R1 × R2) = 24

(R1 + R2) = 10 (From the first equation)

R1 + 24/R1 = 10

(R1)^2 - 10×R1 +24 = 0

(R1 - 4)(R1 - 6) = 0

Thus R1 can be of 4 or 6 ohms. Thus if R1 is of 4 ohms then R2 is of 6 ohms and vice versa.

Thus the two resistances are of 4 and 6 ohms.