How can you connect four of them to produce an equivalent resistance of 0.25 kω?

Question incomplete

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You have a collection of 1.0 kΩ resistors.

How can you connect four of them to produce an equivalent resistance of 0.25 kΩ?

Explanation:

Given that,

We have collection of resistor

R = 1.0 kΩ.

And we want to design an equivalent resistance of

R = 0.25kΩ

We know that,

Series connection of add up resistance and this increases the value of resistance, I. e

Req = R1 + R2 + R3 + ...

While

Parallel resistance add up the reciprocal of resistance and this reduces resistance

So, 1/Req = 1/R1 + 1/R2 + 1/R3 + ...

Now, we want to design 0.25kΩ

Connect four of the resistor in parallel will give a equivalent resistance of 0.25 kΩ

1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4

R1 = R2 = R3 = R4 = 1.0 kΩ

1/Req = 1/1 + 1/1 + 1/1 + 1/1

1/Req = 1+1+1+1

1/Req = 4

Taking reciprocal of both sides ...

Req = ¼ kΩ

This is the required equivalent resistance

So, connect the four of the resistor in parallel will give the required 0.25 kΩ resistance