ten identical resistors connected in parallel have an equivalent resistance of 2 ohm.when they are connected in series what will be its effective resistance?

Question

ten identical resistors connected in parallel have an equivalent resistance of 2 ohm.when they are connected in series what will be its effective resistance?

Answer 1

When resistors are connected in parallel, the equivalent resistance (Rp) can be calculated using the formula:

1/Rp = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

Given that there are ten identical resistors connected in parallel with an equivalent resistance of 2 ohms, we can rewrite the formula as:

1/2 = 1/R1 + 1/R1 + 1/R1 + ... + 1/R1 (10 times)

Simplifying, we get:

1/2 = 10/R1

To find the value of R1, we can rearrange the equation and solve for R1:

2 = R1/10

Multiplying both sides by 10:

20 = R1

Therefore, each resistor in the parallel combination has a resistance of 20 ohms.

When resistors are connected in series, the total or effective resistance (Rs) is found by simply adding up the individual resistances.

Since there are ten resistors connected in series, the effective resistance will be:

Rs = R1 + R2 + R3 + ... + Rn

Rs = 20 + 20 + 20 + ... + 20 (10 times)

Rs = 10 × 20

Rs = 200 ohms

So, when the ten identical resistors are connected in series, the effective resistance will be 200 ohms.

Answer 2

To find the effective resistance when the ten identical resistors are connected in series, you need to understand the concept of series resistance.

When resistors are connected in series, their resistances add up to give the total resistance. So, to get the effective resistance, you need to sum up the resistances of each individual resistor.

Here's how you can calculate it:

Step 1: Find the resistance of one of the identical resistors when connected in parallel. In this case, you are given that the equivalent resistance is 2 ohms for ten resistors connected in parallel.

So, the resistance of one of the identical resistors in parallel is given by:

Resistance in parallel = Equivalent resistance / Number of resistors
Resistance in parallel = 2 ohms / 10 = 0.2 ohms

Step 2: Now, you have the value of resistance for one resistor connected in parallel. Since you have ten resistors connected in series, you need to add up the resistances of all ten resistors.

Effective resistance when connected in series = Resistance of one resistor * Number of resistors

Effective resistance when connected in series = 0.2 ohms * 10 = 2 ohms

So, when the ten identical resistors are connected in series, the effective resistance will be 2 ohms.

Answer 3

1/2=n/x

n=10
x=20 ohms.
ten of these in series will be 200ohms