Question

your friend needs 10 ohms resistance he came to you and asked but you have 40 ohms resistance .how many resistance your friend will ask you ?show that the effective resistance is 10 ohms?

Answer 1

Ans.

4 resistors of resistance 40 Ohm connected in parallel will give the net resistance of 10 Ohm.

Clearly
1/R=1/40+1/40+1/40+1/40
1/R=4/40
R=10 Ohm

Answer 2

Given : 10 Ohm resistance required

Resistor available of  40 ohm

To Find :How many resistors required

Solution:

Resistance in series  gets added R = R1 + R2

Resistance in parallel  1/R = 1/R1 + 1/R2

Let say N resistance of 40 Ω are taken

Then  1/R  = 1/40 + 1/40  + 1/40 +.............+ N times

=> 1/R = N ( 1/40)

=> R = 40/N

R = 10  Ω

40/N = 10

=> N = 40/10

=> N = 4

4 resistors of 40 ohm are required to get  10 Ohm  ( when connected in parallel)

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