Question

20 resistance of 2 ohm each are connected in parallel. Calculate the effective resistance

Answer 1

Given :

• There are 20 resistance of each 20 ohm

To Find :

• Effective Resistance if they are connected in parallel

Solution :

We're given that there are 20 resistors each of resistance 2 ohm. And we've to calculate effective resistance in parallel. God it use formula for resistance in parallel.

⇒1/Rp = 1/R1 + 1/R2 + ....... 1/Rn

So, Putting Values

⇒1/Rp = 1/2 + 1/2 + ....... + 20 times

⇒1/Rp = 20/2

⇒Rp = 2/20

⇒Rp = 1/10

⇒Rp = 0.1

$\therefore$ Effective resistance in parallel is 0.1 ohm

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Additionally Information :

• Resistance in parallel is given by : 1/Rp = 1/R1 + 1/R2 + ..... + 1/Rn

• In parallel combination, resistance give smallest values.

• Formula for serious combination is Rs = R1 + R2 + ..... + Rn

• And in series combination, value of resistance is biggest

Answer 2

Answer :

Given -

• 20 resistors
• Each with resistance 2 ohm
• All of them are connected in parallel

To Find -

• Effective Resistance ?

Solution -

The net effective resistance of resistors connected in parallel connection : 1/Rp = 1/R1 + 1/R2 + ... + 1/Rn.

So, 1/Rp = 1/2 + 1/2 + .... + 1/R20

➸ 1/Rp = 20/2

➸ 1/Rp = 10

➸ 1 = Rp * 10

➸ Rp = 1/10

➸ Rp = 0.1 ohm

So, the net effective resistance of 20 resistors connected in parallel connection is 0.1 ohm.

Additional information -

• The net effective resistance in parallel connection gives the smallest value of resistance.
• The net effective resistance in series connection gives the largest value of resistance.
• The net effective resistance in parallel connection = 1/Rp = 1/R1 + 1/R2 + ... + 1/Rn.
• The net effective resistance in series connection = Rs = R1 + R2 + ... + Rn.