Combination of Resistance

In electric circuits, the resistors are connected in two different ways either in series or parallel combination.

Series combination

If different resistances are connected end to end in a line,then the combination is called series combination.In series combination,same amount of current will pass through all the resistance.

Let three resistance having resistance R1, R2,and R3 are connected in a series with a battery having terminal p.d ‘V’ as shown in figure above. Let V1, Vand V3 be the potential difference across R1, R2,and R3 respectively. Let ‘I’ be the current and ‘R’ be the resistance of the circuit.
Now,
V=V1 +V+ V3
IR=I R+ IR2 + IR3
R= R1 + R+ R3

Thus,in series combination,the net resistance will be equal to sum of individual resistance.

In series combination,the net resistance will be greater than the greatest resistance also.

i.e., Rs = R1 + R2…….. + Rn

If R1 = R2 = Rn

Then, Rs = R + R + R + R….. = nR

Parallel Combination

If current divides at a point, and meet at another point then the combination between two point is called parallel of combination of electricity. In parallel combination potential difference across all the resistance will be equal.


Let 3 resistors having resistance R1 + R2 + R3 are connected in parallel combination with a battery having terminal potential difference ‘V’ as shown in figure. Let I+ I2 and I3 be the current through R1, R2 and R3 respectively. Let ‘I’ be the total current flowing through the circuit and ‘R’ be the net resistance of the circuit. Now,

$$ I= I_1 + I_2 + I_3$$

$$\text{or, V} = \frac{V}{R_1} + \frac{V}{R_2} + \frac{V}{R_3}$$

$$\text{or, } \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$

$$\text{or, } \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_n}$$

Thus the reciprocal of net resistance of the combination is equal to the sum of individual resistance. In this combination, net resistance becomes less than the least resistance of the circuit.

 

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