Question

When ‘n’ equal resistors connected in series the effective resistance becomes 18 Ω and when connected in parallel it becomes 2 Ω. Find the number of resistors and the value of resistance? (a) n=2 R=9 (b) n=6 R=3 (c) n=3 R= 6 (d) n=9 R=2 Plzz answer my question

Answer 1

Given,

When n number of equal resistors are connected in series, the effective resistance becomes 18 Ω and when it is connected in parallel the equivalent resistance becomes 2 Ω

Let the value of each resistor be x,

Case First :-

When it is connected in series:

We know, The combination of resistors connected in series is just the sum of all the resistors.

⇒ x + x + x + ... + xₙ = 18

⇒ n × x = 18

⇒ n = 18/x ...(1)

Case Second :-

When it is connected in parallel, the equivalent resistance becomes 2Ω

Now, The equivalent resistance of resistors connected in parallel is the reciprocal of sum of reciprocal of every resistor.

⇒ 1/x + 1/x + ... + 1/xₙ = 1/2

⇒ n × 1/x = 1/2

⇒ n = x/2 ...(2)

We get, (1) = (2)

⇒ 18/x = x/2

⇒ x² = 36

⇒ x = 6, -6

But, Number of resistors can't be negative.

∴ Number of resistors = 6

Now, Substituting n = 6 in (1),

⇒ n = 18/x

⇒ x = 18/n

⇒ x = 18/6

⇒ x = 3

Now, The resistance of each resistor is 3 Ω

Hence, Option B is correct.