Question

10. A wire that has resistance R is cut into two equal pieces. The two parts are joined in parallel. What is
resistance of the combination ?
11. Calculate the combined resistance in each cage​

Answer 1

Answer:

If we cut a wire of resistance R into n equal parts, the resistance of each new part becomes R/n.

So if the wire is cut into two equal parts, each part will have resistance R/2.

Now these two parts are joined in parallel.

So a resistance R/2 is in parallel with another resistance R/2.

$R_{eq} = \frac{R_{1} R_{2} }{R_{1} + R_{2} }$ = R/4

This is the answer to Q10.

Q11 is not fully clear, but I am assuming you have asked the combined resistance in both cases of series and parallel connection.

In case of series connection, a resistance R/2 is in series with another resistance R/2.

$R_{eq} = R_{1} +R_{2}$ = R

So the equivalent resistance for parallel combination is R/4

And the same for an equivalent series combination is R

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