If a steady current is flowing through a cylindrical element ABC. Choose the correct relationship. [2006]

Question

If a steady current $I$ is flowing through a cylindrical element ABC. Choose the correct relationship. [2006]

Smart Achievers · Accepted Answer

(2)

As both wires are of the same material, $∴$ $I_{A B} = I_{B C}$

(1) $\frac{V_{A B}}{V_{B C}} = \frac{I_{A B} R_{A B}}{I_{B C} R_{B C}} = \frac{R_{A B}}{R_{B C}} = \frac{ρ \frac{ℓ}{2 (π \times 4 r^{2})}}{ρ \frac{ℓ}{2 (π r^{2})}} = \frac{1}{4}$

$∴$ $V_{A B} = \frac{V_{B C}}{4}$

(2) $\frac{P_{B C}}{P_{A B}} = \frac{I^{2} R_{B C}}{I^{2} R_{A B}} = \frac{ρ \frac{ℓ}{2 (π \times 4 r^{2})}}{ρ \frac{ℓ}{2 (π r^{2})}} = \frac{1}{4}$

$∴$ $P_{A B} = 4 P_{B C}$

(3) $\frac{J_{A B}}{J_{B C}} = \frac{\frac{I}{π \times 4 r^{2}}}{\frac{I}{π r^{2}}} = \frac{1}{4};$

$∴$ $J_{B C} = 4 J_{A B}$

(4) $\frac{E_{A B}}{E_{B C}} = \frac{[\frac{V_{A B}}{ℓ / 2}]}{[\frac{V_{B C}}{ℓ / 2}]} = \frac{1}{4}$

$∴$ $E_{B C} = 4 E_{A B}$

Solution

Q.
If a steady current $I$ is flowing through a cylindrical element ABC. Choose the correct relationship. [2006]

1 $V_{A B} = 2 V_{B C}$

2 Power across BC is 4 times the power across AB

3 Current densities in AB and BC are equal

4 Electric field due to current inside AB and BC are equal

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