Relation Between Resistance And Length Important Questions

In the relation between resistance and length the resistance is directly proportional to the length which means that any change in the length of the material will change its value of resistance. Resistivity is indirectly proportional to the temperature. SI unit of resistivity is the ohm. The formula of resistivity is ρ = RA/l.

Resistivity

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Very Short Answer Questions (1 Mark Questions)

Ques. Derive the SI Unit of Resistivity. 

Ans. As We know the formula for resistivity is:

Ρ = RA/L

The unit of resistance is Ohm

The length is a meter 

The area of the cross-section is ‘m²'. 

On putting these values:

= Ohm m²/m 

= Ohm.m.

So, the unit of resistivity is Ohm.m.

Ques. On what basis resistance of a Wire is determined?

Ans. The resistance of a wire is determined on the basis of:

• Length of wire
• Temperature of wire
• Resistivity of material

Ques. State the relationship between resistance and charge.

Ans. The resistance occurs due to collisions between electrons which carry a charge. So it's likely to be more collisions in a longer wire. Whereas, more collisions mean more resistance to the charge flow.

Ques. Do resistance increase with the increase in length?

Ans. Yes, resistance increase with the increase in length. There is a resistance to the flow of an electric current through most of the conductors. The resistance in a wire increases as the length of the wire increases.

Ques. What happens to the resistance of a wire if its length is decreased?

Ans. Resistance is directly proportional to the length of the conductor. The resistance will decrease with the decrease in the length of the wire.

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Short Answer Questions (2 Marks Questions)

Ques. Derive a formula that shows the relation between resistance length and area of cross-section of a conductor.

Ans. The relation between resistance length and area of cross-section of a conductor is specified below

1. The resistance of a conductor (R) is directly proportional to its length (l) for a constant potential difference.

Rαl −(1)

2. The resistance of a conductor is inversely proportional to its cross-section area.

Rα*1/A −(1)

From (1) and (2), we get 

Rα*1/A (at constant temperature)

⇒ R = ρ1/A

Where,  ρ = proportionality constant and it is called specific resistance or resistivity.

The S.I. unit of resistivity is  Ω−m.

Ques. What is the relationship between resistor length and resistance?

Ans. The relationship between resistor length and resistance is as specified; the resistance of a conductor is directly proportional to its length as R ∝ L. Therefore, doubling the length of a conductor will double its resistance whereas halving the length of a conductor would halve its resistance. Also, the resistance of a conductor is inversely proportional to its cross-sectional area (A) as R ∝ 1/A.

Ques. What is the formula for the length of wire and resistance?

Ans. The formula for the length of wire and resistance: R = ρl/A.

Ques. Does resistance depend on length?

Ans. The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Whereas, resistance also depends on the material of the conductor. Ques. What are the 4 factors that affect resistance? Ans. The 4 factors that affect resistance are:-

1. The thickness of the resistor.
2. Material of which the resistor is made.
3. The temperature of the conductor.
4. Length of the resistor.

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