Two wires of equal diameters of resistivity's ρ1 and ρ2 are joined in series. The equivalent res

Step 1: The resistance of a wire is given by the formula $R=rho frac{l}{A}$, where $rho$ is the

Two wires of equal diameters of resistivity's ρ1 and ρ2 are...

Two wires of equal diameters of resistivity's $\rho_{1}$ and $\rho_{2}$ are joined in series. The equivalent resistivity of the combination is.... (A) $\left\{\left(\rho_{1} \ell_{1}+\rho_{2} \ell_{2}\right) /\left(\ell_{1}+\ell_{2}\right)\right\}$ (B) $\left\{\left(\rho_{1} \ell_{2}+\rho_{2} \ell_{1}\right) /\left(\ell_{1}-\ell_{2}\right)\right\}$ (C) $\left\{\left(\rho_{1} \ell_{2}+\rho_{2} \ell_{1}\right) /\left(\ell_{1}+\ell_{2}\right)\right\}$ (D) $\left\{\left(\rho_{1} \ell_{1}+\rho_{2} \ell_{2}\right) /\left(\ell_{1}-\ell_{2}\right)\right\}$

Two wires of equal diameters of resistivity's $\rho_{1}$ and $\rho_{2}$ are joined in series. The equivalent resistivity of the combination is....
(A) $\left\{\left(\rho_{1} \ell_{1}+\rho_{2} \ell_{2}\right) /\left(\ell_{1}+\ell_{2}\right)\right\}$
(B) $\left\{\left(\rho_{1} \ell_{2}+\rho_{2} \ell_{1}\right) /\left(\ell_{1}-\ell_{2}\right)\right\}$
(C) $\left\{\left(\rho_{1} \ell_{2}+\rho_{2} \ell_{1}\right) /\left(\ell_{1}+\ell_{2}\right)\right\}$
(D) $\left\{\left(\rho_{1} \ell_{1}+\rho_{2} \ell_{2}\right) /\left(\ell_{1}-\ell_{2}\right)\right\}$

Key Concepts

Equivalent Resistivity

Equivalent resistivity is used to represent a composite conductor as a homogeneous material that would have the same overall resistance. When different segments of a conductor with the same cross-sectional area but different resistivities are connected in series, the equivalent resistivity can be computed by equating the total resistance of the composite system to that of a uniform piece with the equivalent resistivity and total length.

Resistivity

Resistivity is an intrinsic property of a material that quantifies how strongly the material opposes the flow of electric current. It is independent of the object's shape or size, and when combined with the geometric factors of a conductor, it determines the overall resistance offered by that material to the passage of current.

Resistance of a Conductor

The resistance of a uniform conductor is determined by its resistivity, length, and cross-sectional area through the formula R = ?L/A. This relationship shows that for a given material (with a specified resistivity), a longer conductor will have a higher resistance, while a larger cross-sectional area will reduce the resistance.

Series Combination of Resistors

When resistors are connected in series, their individual resistances add up to give the total resistance of the combination. This principle is useful in analyzing circuits where different materials or sections with distinct properties are joined end-to-end, as the cumulative effect on current flow is directly related to the sum of the individual resistances.

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