Ncert Exercises & Solutions

Two conductors are made of the same material and have the same length. Conductor A is a solid wire of a diameter of 1 mm. Conductor B is a hollow tube of outer diameter 2 mm and inner diameter 1 mm. Find the ratio of resistance R_A to R_B.

Hint: The resistance of the wire depends on the dimensions of the wire.

Step 1: The resistance of the first conductor;

R_{A} = \frac{ρ l}{π (10^{- 3} \times 0.5)^{2}}

Step 2: The resistance of the second conductor;

R_{B} = \frac{ρ l}{π [(10^{- 3})^{2} - (0.5 \times 10^{- 3})^{2}]}

Step 3: Now, the ratio of two resistors is given by;

\frac{R_{A}}{R_{B}} = \frac{{(10^{- 3})}^{2} - (0 .5 \times 10^{- 3})^{2}}{(0 .5 \times 10^{- 3})^{2}} = 3 : 1

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