Question

If the resistance of wire A is four times the resistance of wire B, find the ratio of their cross sectional areas

MSCERT Class 10 General Science Ch4 The Electric Spark

Answer 1

We know that , R = pL/A
Now for wire A , 
R1 = pL1/A1
And for wire B , 
R2 = pL2/A2
Now we are given R1 = 4R2
OR , pL1/A1 = 4pL2/A2
OR , pL1/(πr²)1 = 4pL2/(πr²)2
Now , if L1 = L2 
So , [πr²]2 = 4[πr²]1
So , r2 = 2r1
Thus the ratio of their radii will be r1/r2 = 1/2
and the area of their cross-section will be A1/A2
                                            =(πr²)1 / (πr²)2
                                            = [r1]²/[r2]² = 1²/2² = 1/4