CDS (II) 2021 General Knowledge · Question 4 of 120

Correct — B, gets doubled. This is the school laboratory result about what resistance depends on, run backwards. For a uniform wire, resistance is proportional to length and inversely proportional to area of cross-section, so halving the length of the same nichrome wire halves its resistance. The cell in the circuit holds the potential difference across the wire essentially fixed, and Ohm's law then gives current as V divided by R; halve R and the current doubles. The ammeter is in series and reads that current, so its reading doubles. NCERT's Activity 11.3 sets up precisely this circuit — a cell, an ammeter, a nichrome wire of length l and a plug key — and records the mirror-image observation: the ammeter reading decreases to one-half when the length of the wire is doubled. Nothing else in the circuit has changed. The resistivity of nichrome is a property of the material and is unaffected by cutting the wire; only the geometry has changed, and only the length part of it.

• (a)decreases to one-half. — This is what happens when the wire is made twice as long, not half as long. The reading tracks the current, which moves opposite to resistance.
• (c)decreases to one-third. — No factor of three appears anywhere. Halving the length changes resistance and current by a factor of two, and in the direction that raises the current.
• (d)remains unchanged. — That would require resistance to be independent of length. Resistance for a uniform conductor is directly proportional to length, so shortening the wire must change the current.

The resistance of a uniform conductor depends on three things — its length, its area of cross-section, and the material it is made of. Written out, R equals resistivity times length divided by area. Resistivity belongs to the material and is unchanged by cutting or stretching the sample; length and area belong to the particular piece of wire. Ohm's law, V equals IR, then converts a change in resistance into a change in the current a fixed source can drive.

Two steps have to be kept in the right order, and reversing either one produces a listed option. First, shorter means less resistance, because there is less material for the electrons to be scattered by along the way. Second, less resistance at fixed voltage means more current. Candidates who track only the first step and then answer with the direction of the resistance change land on (a). Nichrome is chosen here for a reason, and is worth remembering: it is an alloy of nickel, chromium, manganese and iron with a high resistivity, which is why it is the material of heating elements in irons, toasters and room heaters, and why it makes a good visible-effect resistor in a school circuit. Note also that resistivity itself would not change if the wire were replaced by a longer or thicker piece of the same nichrome — a distinction examiners test on its own.

• For a uniform conductor, resistance is directly proportional to length and inversely proportional to area of cross-section.
• NCERT's Activity 11.3 records that the ammeter reading decreases to one-half when the length of the nichrome wire is doubled; this item is that observation reversed.
• Resistivity is a property of the material and its temperature, not of the size or shape of the sample.
• Nichrome is an alloy of nickel, chromium, manganese and iron, and its high resistivity is why it is used in heating elements.
• The order of resistivity at room temperature runs silver below nichrome below glass — conductor, alloy, insulator.

• Answering with the direction the resistance moves instead of the direction the current moves.
• Confusing resistance with resistivity — cutting a wire changes the first and leaves the second untouched.
• Forgetting that thickness matters too: doubling the area of cross-section also halves the resistance.

As a length-or-thickness change with an ammeter reading to predict, as a resistivity ordering item, or as a numerical using R equal to resistivity times length over area.

• practice — not a real PYQ

  A uniform wire of resistance R is stretched so that its length is doubled and its area of cross-section is halved. Its new resistance is

  • (a)R/2
  • (b)2R
  • (c)4R
  • (d)R

  Answer(c) 4R — resistance rises by a factor of two for the doubled length and by another factor of two for the halved area.

• practice — not a real PYQ

  Which one of the following does not change when a copper wire is cut into two equal halves?

  • (a)Its resistance
  • (b)Its resistivity
  • (c)Its length
  • (d)Its mass

  Answer(b) Its resistivity — resistivity is a property of the material and its temperature, not of the size of the piece.