Question

The equivalent resistance in series combination is:
(This question has multiple correct option)
Smaller than the largest resistance
Larger than the largest resistance
Smaller than the smallest resistance
Larger than the smallest resistance

Answer 1

A resistor can be defined as an electrical component that has the capacity to convert current into voltage and vice-versa. The equivalent resistance in a series combination is the sum of all the individual resistances while in case of parallel combination the inverse of equivalent resistance is the sum of all the individual resistances.

Complete step-by-step solution:
Resistances are assumed to be connected in a series combination when they are connected in a line. The equivalent resistance in series combination is the sum of all the resistances. Thus, the equivalent resistance will always be greater than the value of any individual resistance. Hence, we can conclude that the equivalent resistance will be larger than both the largest and the smallest resistance. Therefore, options $B$ and $D$ are correct.
For example, let us consider three resistances $1\Omega$, $2\Omega$ and $3\Omega$ to be connected in a series combination in a circuit which has some current flowing through it and some voltage is connected to the circuit, then their equivalent resistance would be:
$\begin{aligned} & {{R}_{eq}}=(1+2+3)\Omega \\\ & \Rightarrow {{R}_{eq}}=6\Omega \\\ \end{aligned}$
We can observe that the equivalent resistance is largest among all the individual resistances. Hence, we can conclude that the equivalent resistance will be larger than both the largest and the smallest resistance.

Note: The voltage difference across all the individual resistors that are connected in a series combination is different from each other, while in a parallel combination, the voltage difference across each individual resistor is equal. Although the amount of energy used by each resistor connected in a series combination is equal.