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Q.

Is it true that equivalent resistance in parallel combinations of resistors is always less than the least resistance of any resistor in the circuit?

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a

True

b

False

answer is A.

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Detailed Solution

The above statement is True.
Resistors are said to be connected in parallel when both of their terminals are respectively connected to each terminal of the other resistor or resistors. When the resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of reciprocals of individual resistances, which makes it the least of all the individual resistances. Mathematically if

R_{p}

represents the equivalent resistance of the resistors

R_{1}, R_{2}, R_{3}, \dots, R_{N}

connected in parallel, then the equivalent resistance is given by

\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \dots + \frac{1}{R_{N}}

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