The current enters at A and comes out at D . Some of the resistances are shown. What should be resistance of wire C B so that it draws double of the current that enters the wire B F .

Step-by-step solution

Let current in A B be I 1 , in B F be I 2 , in B C be 2 I 2 , in F C be I 3 , in F E be I 3 and in C D be I 3 + 2 I 2 , at point B , I 1 = 3 I 2 , at point, F , I 2 = 2 I 3 First, convert the circuit in simple form and using current law given by Kirchhoff's, Along, A B C D , V A - V D = V = I 1 2 R 5 + I 2 R 5 + I 3 R 5 + I 3 + 2 I 2 R 5 = 2 I 2 R Along, A B C D , V A - V D = V = 2 I 2 R = I 1 2 R 5 + 2 I 2 R ' + I 3 + 2 I 2 R 5 ⇒ 2 I 2 R ' = 3 10 I 2 R ⇒ R ' = 3 20 × R