Match the following:
The following table gives the lengths of four copper rods at the same temperat…

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Match the following:
The following table gives the lengths of four copper rods at the same temperature, their diameters, and the potential differences between their ends.
RodLengthDiameterPotentialDifference1L3 dV22 Ld3 V33 L2 d2 V43 LdV
Correctly match the physical quantities mentioned in the left column with the rods as marked.
Column IColumn II(A)Greatest Drift speed of the electrons.(P)Rod 1(B)Greatest Current(Q)Rod 2(C)Greatest rate of thermal energy produced(R)Rod 3(D)Greatest Electric field(S)Rod 4

CGP EDU Academic Team · Accepted Answer

The correct answer is A. Step 1: Understanding the relation between potential difference, current, and drift speedWe can relate the drift speed of electrons, current, and electric field using the following formulas:Current, $I = nAq v_d$, where $n$ is the number density of charge carriers, $A$ is the cross-sectional area, $q$ is the charge of an electron, and $v_d$ is the drift speed.Electric field, $E = \frac{V}{L}$, where $V$ is the potential difference and $L$ is the length of the rod.The power or thermal energy produced in a conductor can be expressed as $P = I^2 R$, where $R$ is resistance, which varies with length and cross-section.Step 2: Evaluating the provided rodsNow let’s evaluate each rod's parameters:Rod 1: Length = $L$, Diameter = $3d$, $A = \frac{\pi (3d/2)^2}{4} = \frac{9\pi d^2}{16}$, $E = \frac{V}{L} = \frac{V}{L}$Rod 2: Length = $2L$, Diameter = $d$, $A = \frac{\pi (d/2)^2}{4} = \frac{\pi d^2}{16}$, $E = \frac{3V}{2L}$Rod 3: Length = $3L$, Diameter = $2d$, $A = \frac{\pi (d)}{4} = \frac{\pi (2d/2)^2}{4} = \frac{\pi d^2}{4}$, $E = \frac{2V}{3L}$Rod 4: Length = $3L$, Diameter = $d$, $A = \frac{\pi d^2}{16}$, $E = \frac{V}{3L}$Step 3: Determining greatest drift speed, current, thermal energy, and electric fieldThe drift speed $v_d$ is inversely related to length and the area. Rod 2 has the largest current due to the smallest area and longer length, thus greatest drift speed.Current is greatest in the rod with the largest diameter and higher potential difference, Rod 2 as well.The rate of thermal energy is given by $P = I^2 R$, where larger currents and resistances leads to greater thermal losses. Thus rod 3 has greatest rate.Finally, we find that the electric field is highest in Rod 2 as it has the highest voltage over its length.Step 4: Matching quantities to rodsThus we can conclude:A matches with Rod 2 (Greatest Drift Speed)B matches with Rod 3 (Greatest Current)C matches with Rod 4 (Greatest rate of thermal energy produced)D matches with Rod 1 (Greatest Electric Field)Therefore, we find that options match correctly. Thus, the answer is Rod 1 (A), Rod 2 (B), Rod 3 (C), Rod 4 (D). Therefore, the first matching component to each rod is the correct answer.

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Rod	Length	Diameter	Potential Difference
1	L	3 d	V
2	2 L	d	3 V
3	3 L	2 d	2 V
4	3 L	d	V

	Column I		Column II
(A)	Greatest Drift speed of the electrons.	(P)	Rod 1
(B)	Greatest Current	(Q)	Rod 2
(C)	Greatest rate of thermal energy produced	(R)	Rod 3
(D)	Greatest Electric field	(S)	Rod 4

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