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

**(R**_{1 }R_{2 })/**( R**equivalent resistance is_{1 }+ R_{2 })**(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 ΩFig. 2 |

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