[93]Is it true that in a series combination for a resistor, the equivalent resistance will be the sum of individual resistance, which gives more value than the parallel combination of the resistors?

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[93]

Is it true that in a series combination for a resistor, the equivalent resistance will be the sum of individual resistance, which gives more value than the parallel combination of the resistors?

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Detailed Solution

The above statement is True.
Resistance is the property of materials which oppose the flow of current. Resistances are connected end to end in a series arrangement so that the current flowing through each one is the same. In contrast, the resistances in a parallel combination are connected to receive an equal amount of voltage. In a series combination for a resistor, the equivalent resistance will be the sum of individual resistance, which gives more value than the parallel combination of the resistors.

{\Rightarrow R}_{eff} = R_{1} + R_{2} + R_{3} + \dots . .

For n identical resistors with resistance

R_{eff} = n R_{}

.
Also, the equivalent resistor of a parallel combination is

\Rightarrow \frac{1}{R_{eff}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + . . . . .

The equation clearly states that in the parallel combination, the current is divided, and the equivalent resistance is always the reciprocal addition. Hence the value always remains the smallest compared to a series combination.

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