TS EAMCET · Physics · Current Electricity

A tapered bar of length $L$ and end diameters $D_{1}$ and $D_{2}$ is made of a material of electrical resistivity $ρ$ . The electrical resistance of the bar is

A $\frac{4 ρ L}{π {(D_{1} + D_{2})}^{2}}$
B $\frac{4 ρ L}{π {(D_{1} - D_{2})}^{2}}$
C $\frac{ρ π \sqrt{D_{1} D_{2}}}{4 L^{2}}$
D $\frac{4 ρ L}{π D_{1} D_{2}}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{4 ρ L}{π D_{1} D_{2}}$

Step-by-step Solution

Detailed explanation

The shape of the conductor is of frustum whose area is A=A1A2=π4D12×π4D22=π4×D1D2 R=ρLA=4ρLπD1D2

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A tapered bar of length L and end diameters D1 and D2 is made of a material of electrical resistivity ρ. The electrical resistance of the bar is

Step-by-step Solution

A tapered bar of length $L$ and end diameters $D_{1}$ and $D_{2}$ is made of a material of electrical resistivity $ρ$ . The electrical resistance of the bar is