Question

1m long metallic wire is broken into two unequal parts P and Q.P part of the wire is uniformly extended into another wire R.length of R is rwice of P and the resistance of R is equal to that of Q.Find the ratio of the resistance of P and R and also the ratio of lengths of P and Q.​

Answer 1

Answer:

The ratio of the resistance of P and R is 1:4

the ratio of lengths of P and Q is 1:4

Explanation:

According to the problem the length of the wire is 1 m

it is broken onto equal parts P and Q

let the length of P = x

Therefore length Q = y = 1-x

Let the resistance per meter of the wire is r

The resistance of P = R(P)= rx

The resistance of Q = R(Q)= r(1-x)

The P makes its length twice to make the wire R the cross sectional area reduces to half

R(R)= 4R(P)= 4rx

According to the problem

R(R)= R(Q)

=> 4rx= r(1-x)

=> x = 1/5

therefore y= 1-x=  4/5

Therefore the resistance ratio of  P and R will be  = R(P)/R(R)

                                                                =  rx/4rx = 1/4 = 1:4

The length ration of P and Q will be = x/y= 1/5/4/5= 1:4