# Does anyone know how to answer this electric physics question if someone could help me and work it out for me step by step that be great?

A wire of uniform cross-section has a resistance of 0.025 . What would be the resistance of a wire of the same material which was twice as long and with twice the diameter?

• ?
5 days ago

First of all as a (presumed) physics student, U realize that measured quantities have UNITS and these units should always accompany the numerical in order to identify what the measurement scale is (i.e. units).

So that reported resistance would be: 0.025 Ω {ohms}

Solution to question:

Taking the length factor, first, doubling the length would double the resistance because the wire’s resistance would simply double. A wire’s resistance is directly proportional to its length.

Doubling the diameter would quadruple the wire’s cross-sectional area, which would (like water flowing thru a larger diameter pipe) lower its resistance to 1/4 of its former value. Cross-sectional area is the critical factor.

The combinational effect of length & diameter changes would be the product of their individual change factors:

2 x (1/4) = 2/4 = 0.5 <= combined factor effect

Therefore the resistance of the longer and thicker wire = 0.025(0.5) = 0.0125 Ω ANS

• ?
5 days ago

The answer is 0.0125 (ohms I guess), here is how: Resistance of wire = (resistivity)*(length)/(cross section area), and cross section area = pi*r² = pi*(dia/2)² = (pi/4)*(diameter)².

So if the new length is 2 times, that multiplies resistance x 2, but then dividing by (2*dia)² results in dividing by 4, so the net result is the new wire has half resistance of the old wire, so it is 0.0125 Ω

• Morningfox
5 days ago

0.025 is not a resistance, it is just a number. Do you mean 0.025 ohms?

Twice the length –> twice the resistance.

Twice the diameter –> four times the cross-section area –> 1/4 the resistance.

2 * (1/4) = 1/2

• oubaas
5 days ago

R2 = R1*2/2^2= R1/2