Resistivity

Copper metal is a good conductor of electricity because copper atoms in copper metal:

• have gained an extra or “free” electron

• are ionised so that both ions and “free” electrons can move

• have a negative charge because of the “free” electrons

• have lost an electron to form positive ions and “free” electrons

A wire has a resistance R.

What is the resistance when both the length and radius of the wire are doubled?

• R/4

• R/2

• 2R

• 4R

A cylindrical conductor of length l, diameter D, and resistivity ρ has a resistance R.

What is the resistance of another cylindrical conductor of length l, diameter D/2, and resistivity ρ?

• 8R

• 4R

• 2R

• R

Two resistors R1 and R2 are made of wires of the same material. The wire used for R1 has half the diameter and is twice as long as the wire used for R2.

What is the value of the ratio resistance of R1 / resistance of R2?

• 8

• 4

• 1

• 0.5

Two resistors are both uniform cylinders of equal length made from the same conducting putty.

The diameter of Y is twice that of X. The resistance of Y is R.

What is the total resistance of the two resistors connected in series?

• 4R / 5

• 3R

• 4R

• 5R

A 1.5 m length of wire has a cross-sectional area 5.0 × 10^–8 m². When the potential difference across its ends is 0.20 V, it carries a current of 0.40 A. The resistivity of the material from which the wire is made is

• 6.0 × 10⁷ Ω m

• 1.7 × 10^–8 Ω m

• 1.1 × 10⁶ Ω m

• 9.4 × 10^–7 Ω m

When a constant potential difference (pd) is applied across the ends of a uniform wire there is a current I in the wire.

The wire is replaced by one made from the same material, but of double the length and double the diameter. The same pd is applied across the ends.

What is the new current?

• 4I

• 2I

• I / 2

• I / 4

• R / 9

• R / 3

• 2R / 3

• 3R / 2