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Q.

A wire that has resistance R is cut into two equal pieces; the two parts are joined in parallel. What is the resistance of the combination?

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a

\frac{R}{4}

b

\frac{R}{2}

c

\frac{R}{8}

d

R

answer is D.

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Detailed Solution

Let the length of the wire be 'l' and area of the cross-section be 'A' and resistivity of the material be ρ
Therefore R =

\frac{ρ l}{A}

When it is broken then take each of the piece: -
Its resistance =

\frac{ρ l}{2 A}

=

\frac{R}{2}

When joined in parallel net resistance =

\frac{R}{4}

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