The picture shows a battery connected to two wires in parallel. Both wires are m

Question

The picture shows a battery connected to two wires in parallel. Both wires are made of the same material and are of the same length, but the diameter of wire A is twice the diameter of wire B. The resistance of wire B is four times as large as the resistance of wire A. The power dissipated in wire A is 16 times the power dissipated in wire B. The current through the battery is five times larger than the current through wire B. The voltage drop across wire B is larger than the voltage drop across wire A. The resistance of wire B is twice as large as the resistance of wire A.

Explanation / Answer

resistance is inversely proportional to area.

R= *(l/A) here is the resistivity of the material, l is the length and A is the area of cross section,

now the wires are of the same length and same material so

Ra/Rb= (Ab/Aa)

(Ab/Aa) = 1/4

so

Ra = (1/4) Rb hence the resistance of wire B is 4 times larger than the resistance of wire A,

let the battery be having a voltage V,

so current through A = 4V/Rb , Current thorugh B = V/Rb , net current through battery = Inet =(4V/R+V/Rb) = 5V/Rb

hence through the battery 5 times the current of wire B flows.

power dissipated is V2/R , and since the resistance of wire B is 4 times the resistance of wire A the power dissipated in wire B is 4 times less than that in wire A.

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