For the circuit shown in figure-1 find out the equivalent resistance across the terminals ab, bc, cd, da and bd. Network Reduction Technique mail to know more Problem # 1 a b d c 2  4  6  8  Figure-1

Let us look at the terminals ‘ab’: Branches ad, dc and cb are in series. Why? Since same current flows through these elements. So what will be the equivalent resistance of these three elements? That will be, (8+4+6)=18  Now look, this 18  resistance is in parallel with branch ab of 2  resistance. Isn’t so? Yes, because potential difference across 18  and 2  is same. So the overall resistance across ‘ab’ terminals, mail to know more a b 2  18  After first reduction a b 1.8  After final reduction a b d c 2  4  6  8  Figure-1

Now look at the terminals ‘bc’: In this case branches ba, ad and dc are in series. So the equivalent resistance of these three elements is =(2+8+4)=14  Now look, this 14  resistance is in parallel with branch bc of 6  resistance. So the overall resistance across ‘bc’ terminals, mail to know more a b d c 2  4  6  8  Figure-1 After first reduction b c 6  14  After final reduction 4.2  b c

Now look at the terminals ‘cd’: Similarly in this case branches ad, ab and bc are in series. Equivalent resistance of these three elements is =(8+2+6)=16  Again this 16  resistance is in parallel with branch dc of 4  resistance. So the overall resistance across ‘ab’ terminals, mail to know more a b d c 2  4  6  8  Figure-1 d c 16  4  After first reduction d c 3.2  After final reduction

Now look at the terminals ‘ad’: In this case branches ab, bc and cd are in series. Therefore equivalent resistance of these three elements is =(2+6+4)=12  This 12  resistance is in parallel with branch ad of 8  resistance. So the overall resistance across ‘ad’ terminals, mail to know more a b d c 2  4  6  8  Figure-1 After first reduction a d 12  8  After final reduction 4.8  a d

Now look at the terminals ‘bd’: In this case branch ab is in series with ad and similarly branch bc is in series with branch cd. Finally these combined resistances are in parallel with each other. That is, (8+2)=10  resistor is in parallel with (6+4)=10  resistor. Therefore equivalent resistance across bd terminals, mail to know more Figure-1 After first reduction b d 10  10  After final reduction 5  b d a b d c 2  4  6  8 

1. Find out the equivalent resistance across the terminals ab of the circuit in figure-2. 2. Reduce the circuit to find out the equivalent resistance across the terminals ab, ac and bc of the circuit in figure-3. Assignment 3. Find out the equivalent resistance across the terminals ab ac and bc of the circuit in figure-4. b a 2  4  c 4  2  3  Figure-4 3  Marks:2 Marks:2+2+2 Marks:1+1+1 mail to know more Figure-2 12  a b 4  6  8  2  12  Figure-3 c b a 2  4  4  2  4  3  5  5  3 