The resistance of the two resistors when connected in parallel will be equal to 8R.
What is resistance?
The resistance of a wire is defined as the restriction to the flow of the charge or current offered by the wire.
It is given in the question that
Two resistors, each of length 2l and mass m/2 are then created from the same volume of the metal.
The formula for the resistance is given by
\(R=\dfrac{\rho A}{l}\)
According to the question two resistances are
\(R_1=\dfrac{\rho A/2}{l/2}=\dfrac{\rho A}{4l}\)
\(R_2=\dfrac{\rho A/2}{l/2}=\dfrac{\rho A}{4l}\)
From the parallel combination of resistances we have
\(\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\)
\(\dfrac{1}{R_{eq}}=\dfrac{1}{\dfrac{\rho A}{4l}}+\dfrac{1}{\dfrac{\rho A}{4l}}\)
\(\dfrac{1}{R_{eq}}=\dfrac{4l}{ {\rho A} }+\dfrac{4l}{ {\rho A} }\)
\(\dfrac{1}{R_{eq}}=\dfrac{4}{\dfrac{\rho A}{l}}+\dfrac{4}{\dfrac{\rho A}{l}}\)
\(\dfrac{1}{R_{eq}}=\dfrac{4}{ R}+\dfrac{4}{ R}\)
\(R_{eq}=8R\)
Hence the resistance of the two resistors when connected in parallel will be equal to 8R.
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