Summary of Series and Parallel circuits

The table 1 gives the equivalent at 'n' basic elements in series.

Table . 1  Series combination of elements

The table 2 gives the equivalent at 'n' basic elements in parallel.

Table . 2  Parallel combination of elements

 Key point : The current through series combination remains same and voltage gets divided while in parallel combination voltage across combination remains same and currents gets divided.

Example 1 :

       Find the equivalent resistance between the tow point A and B shown in the Fig. 1.

Fig. 1                

Solution : Identify combinations of series and parallel resistances.

       The resistance 5 Ω and 6 Ω are in series, as going to carry same current.

       So equivalent resistance is 5+6 = 11 Ω

      While the resistance 3 Ω, 4 Ω and 4 Ω are in parallel, as voltage across them same but current divides.

      .^..    equivalent resistance is,                1/R = 1/3 + 1/4 + 1/4 =10/12

      .^..                                                         R = 12/10 = 1.2 Ω

       Replacing these combinations redraw the figure as shown in the Fig. 2(a).

       Now again 1.2 Ω and 2 Ω are in series so equivalent resistance is 2 + 1.2 = 3.2 Ω while 11 Ω and 7 Ω are in parallel.

      Using formula (R₁  R₂ )/( R₁ + R₂ ) equivalent resistance is (11x 7)/(11+7) = 77/18 = 4.277 Ω

       Replacing the respective combinations redraw the circuit as shown in the Fig. 2(b). 

       Now 3.2 and 4.277 are in parallel.

       Replacing them by (3.2 x 4.227)/(3.2 + 4.227 ) = 1.8304 Ω

                                                  R_AB  = 1+1.8304 = 2.8304 Ω

Fig. 2